Abstract m-space

In mathematics, specifically in order theory and functional analysis, an abstract m-space or an AM-space is a Banach lattice $(X,\|\cdot \|)$ whose norm satisfies $\left\|\sup\{x,y\}\right\|=\sup \left\{\|x\|,\|y\|\right\}$ for all x and y in the positive cone of X.

We say that an AM-space X is an AM-space with unit if in addition there exists some $u \geq 0$ in X such that the interval $[- u, u] := {z \in X : - u \leq z and z \leq u}$ is equal to the unit ball of X; such an element u is unique and an order unit of X.^[1]

Examples

The strong dual of an AL-space is an AM-space with unit.^[1]

If X is an Archimedean ordered vector lattice, u is an order unit of X, and p_u is the Minkowski functional of $[u,-u]:=\{x\in X:-u\leq x{\text{ and }}x\leq x\},$ then the complete of the semi-normed space (X, p_u) is an AM-space with unit u.^[1]

Properties

Every AM-space is isomorphic (as a Banach lattice) with some closed vector sublattice of some suitable $C_{\mathbb {R} }\left(X\right)$ .^[1] The strong dual of an AM-space with unit is an AL-space.^[1]

If X ≠ { 0 } is an AM-space with unit then the set K of all extreme points of the positive face of the dual unit ball is a non-empty and weakly compact (i.e. $\sigma \left(X^{\prime },X\right)$ -compact) subset of $X^{\prime }$ and furthermore, the evaluation map $I:X\to C_{\mathbb {R} }\left(K\right)$ defined by $I(x):=I_{x}$ (where $I_{x}:K\to \mathbb {R}$ is defined by $I_{x}(t)=\langle x,t\rangle$ ) is an isomorphism.^[1]

References

^ ^a ^b ^c ^d ^e ^f Schaefer & Wolff 1999, pp. 242–250.

Bibliography

Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.

Functional analysis (topics – glossary)

Spaces

Banach Besov Fréchet Hilbert Hölder Nuclear Orlicz Schwartz Sobolev Topological vector
Properties	Barrelled Complete Dual (Algebraic / Topological) Locally convex Reflexive Separable

Theorems

Operators

Algebras

Open problems

Applications

Advanced topics

Category

v t e Ordered topological vector spaces
Basic concepts	Ordered vector space Partially ordered space Riesz space Order topology Order unit Positive linear operator Topological vector lattice Vector lattice
Types of orders/spaces	AL-space AM-space Archimedean Banach lattice Fréchet lattice Locally convex vector lattice Normed lattice Order bound dual Order dual Order complete Regularly ordered
Types of elements/subsets	Band Cone-saturated Lattice disjoint Dual/Polar cone Normal cone Order complete Order summable Order unit Quasi-interior point Solid set Weak order unit
Topologies/Convergence	Order convergence Order topology
Operators	Positive State
Main results	Freudenthal spectral

Read other articles:

Bahasa Kurmanji

Cari artikel bahasa Cari berdasarkan kode ISO 639 (Uji coba) Kolom pencarian ini hanya didukung oleh beberapa antarmuka Halaman bahasa acak Bahasa Kurmanji Kurmancî, Kurdiya Jorîn Kurmanji Dituturkan diIran, Irak, SuriahPenutur15 juta di Turki (2009)[1]Mungkin 5 juta tempat lain, termasuk 2,8 juta di Irak (2004), 940.000 di Suriah (1993), dan 350.000 di Iran (1988)[1] Rincian data penutur Jumlah penutur beserta (jika ada) metode pengambilan, jenis, tang...

Élections sénatoriales françaises de 2014

2011 2017 Élections sénatoriales françaises de 2014 178 des 348 sièges du Sénat 28 septembre 2014 UMP – Jean-Claude Gaudin Sièges obtenus 144 14 SOC – Didier Guillaume Sièges obtenus 111 17 UDI-UC – François Zocchetto Sièges obtenus 43 12 CRC – Éliane Assassi Sièges obtenus 18 3 RDSE – Jacques Mézard Sièges obtenus 13 6 ECO – Jean-Vincent Placé Sièges obtenus 10 Composition du...

الدوري المنغولي لكرة القدم 2010

هذه المقالة تحتاج للمزيد من الوصلات للمقالات الأخرى للمساعدة في ترابط مقالات الموسوعة. فضلًا ساعد في تحسين هذه المقالة بإضافة وصلات إلى المقالات المتعلقة بها الموجودة في النص الحالي. (يوليو 2023) يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة ...

العلاقات الزامبية الكمبودية

العلاقات الزامبية الكمبودية زامبيا كمبوديا زامبيا كمبوديا تعديل مصدري - تعديل العلاقات الزامبية الكمبودية هي العلاقات الثنائية التي تجمع بين زامبيا وكمبوديا.[1][2][3][4][5] مقارنة بين البلدين هذه مقارنة عامة ومرجعية للدولتين: وجه المقارن...

أيزو 14000

ISO 14000 عائلة من المعايير ذات الصلة للإدارة البيئية الموجودة لمساعدة المنظمات (أ) تقليل كيفية تأثير العمليات (الأعمال الصناعية، إلخ.) سلبا على البيئة (أي تسبب تغيرات سلبية في الهواء أو الماء أو الأرض)؛ (ب) الامتثال للقوانين المعمول بها واللوائح الأخرى الموجهة بيئيا؛ و (ج) تحسن �...

Boardwalk Empire

Boardwalk Empire Logo noir & blanc de la série. Données clés Titre original Boardwalk Empire Genre Série dramatique Création Terence Winter Production Mark Wahlberg Acteurs principaux Steve BuscemiMichael PittKelly MacdonaldStephen GrahamMichael Shannon Pays d'origine États-Unis Chaîne d'origine HBO Nb. de saisons 5 Nb. d'épisodes 56 Durée 49-72 minutes Diff. originale 19 septembre 2010 – 26 octobre 2014 Site web http://www.hbo.com/boardwalk-empire modifier - modifier le code ...

Dhini Aminarti

Dhini AminartiLahirDhini Aminarti Maulana29 Mei 1983 (umur 40)Cirebon, Jawa Barat IndonesiaKebangsaanIndonesiaPekerjaanPemeranpresenterTahun aktif1998—sekarangSuami/istriDimas Seto (m. 2009) Dhini Aminarti Maulana, S.Psi. (lahir 29 Mei 1983) adalah pemeran dan presenter Indonesia. Kehidupan pribadi Dhini menyelesaikan studinya di Universitas Paramadina dengan mengambil jurusan S-1 Psikologi.[1] Dhini pernah berpacaran dengan aktor dan model ...

Kereta rel listrik i9000

KRL KfW i9000KRL KfW i9000 meninggalkan Stasiun Palur dan akan diantar menuju area Stabling di Solo BalapanBeroperasiYaPembuatPT INKABombardier TransportationDigantikan olehTokyo Metro seri 05 di Lin Tanjung PriokTahun pembuatan2011Mulai beroperasi24 Agustus 2011-sekarangTahun rehabilitasi2019-2020Formasi4 atau 8 kereta per setNomor armada40 unit (K3 1 11 01-K3 1 11 40)Kapasitas628 penumpang (rata-rata)OperatorPT Kereta Api Indonesia (Persero)KAI CommuterJalurY Commuter Line YogyakartaData te...

Windows XP

Windows XPVersi dari sistem operasi Windows NTPembangunMicrosoftModel sumberSumber penutup, sumber bersama[1]Dirilis kemanufaktur24 Agustus 2001; 22 tahun lalu (2001-08-24)Ketersediaanuntuk umum25 Oktober 2001; 22 tahun lalu (2001-10-25)[2]Rilis terbaru5.1 (Build 2600: Service Pack 3) / 21 April 2008; 16 tahun lalu (2008-04-21)[3]Metode updateWindows UpdateWindows Server Update Services (WSUS)System Center Configuration Manager (SCCM)PlatformIA-32, x86-6...

Ираклеониты

Ираклеониты — ученики гностика Ираклеона (II век). Упоминаются как особая секта Епифанием и Августином; при крещении и миропомазании они соблюдали обряд помазания елеем и при этом произносили воззвания на арамейском языке, которые должны были освободить душу от власт�...

Teen Beach Movie

Teen Beach MoviePoster FilmSutradaraJeffrey HornadayProduserRobert F. PhillipsDitulis oleh Vince Marcello Mark Landry Robert Horn Pemeran Ross Lynch Maia Mitchell Grace Phipps Garrett Clayton Jordan Fisher John Deluca Chrissie Fit Kevin Chamberlin Steve Valentine SinematograferMark IrwinDistributorDisney Channel Original MovieTanggal rilis19 Juli 2013Durasi95 MenitNegaraAmerika SerikatBahasaInggris Teen Beach Movie merupakan sebuah film Disney Channel Original Movie Amerika Serikat yang akan ...

Maureen O'Sullivan

Maureen O'Sullivanfrom the trailer for Woman Wanted (1935)LahirMaureen Paula O'Sullivan(1911-05-17)17 Mei 1911Boyle, County Roscommon, IrelandMeninggal23 Juni 1998(1998-06-23) (umur 87)Arizona, U.S.PekerjaanAktrisTahun aktif1930–1994Suami/istriJohn Farrow (1936–1963) (his death)James Cushing (1983–1998) (her death) Maureen O'Sullivan (17 Mei 1911 – 23 Juni 1998) merupakan seorang aktris berkebangsaan Irlandia. Dia dilahirkan dengan nama Maureen Paula O'Sulliva...

Baihao Yinzhen

Baihao Yinzhen dari Yunnan. Fuding Baihao Yinzhen. Baihao Yinzhen (Hanzi sederhana: 白毫银针; Hanzi tradisional: 白毫銀針; Pinyin: báiháo yínzhēn; Wade–Giles: pai2-hao2 yin2-chên3; dilafalkan [pǎɪ.xɑ̌ʊ ǐn.tʂə́n]), sering juga disebut Jarum Perak Rambut Putih, adalah teh putih yang diproduksi di Provinsi Fujian, Tiongkok.[1] Teh jarum perak atau Baihao Yinzhen yang biasanya disingkat menjadi Yin Zhen saja, adalah jenis teh ...

Elizabeth Rona

Hungarian chemist (1890–1981) Elizabeth RonaBornErzsébet Róna(1890-03-20)20 March 1890Budapest, Hungary, Austria-HungaryDied27 July 1981(1981-07-27) (aged 91)Oak Ridge, Tennessee, U.S.Nationality Hungarian American (naturalized 1948) Other namesElisabeth RónaOccupationNuclear chemistYears active1914–1976Known forPolonium extraction and investigating radioactivity in sea water Elizabeth Rona (20 March 1890 – 27 July 1981) was a Hungarian nuclear chemist, known for ...

Le front de libération populaire

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article may require cleanup to meet Wikipedia's quality standards. The specific problem is: Subject of article is not properly defined or explained. Please help improve this article if you can. (March 2016) (Learn how and when to remove this message) This article relies largely or entirely on a single source. Relevant discussion may be ...

Historia de Portugal

revuelta de las monjas odivelas Este artículo o sección necesita referencias que aparezcan en una publicación acreditada. Busca fuentes: «Historia de Portugal» – noticias · libros · académico · imágenesEste aviso fue puesto el 12 de marzo de 2011. Artículo principal: PortugalBandera del Condado de Portucale La historia de Portugal es la propia de una nación europea cuyos orígenes se remontan a la Baja Edad Media, que amplió sus territorios durante la Er...

John Lethbridge

English wool merchant who invented a diving machine in 1715 For other people named John Lethbridge, see John Lethbridge (disambiguation). A replica of the Lethbridge diving machine at the Cité de la Mer ('City of the Sea') in Cherbourg, France. John Lethbridge (1675–1759) invented the first underwater diving machine in 1715. He lived in the county of Devon in South West England and reportedly had 17 children.[1] He is the subject of the Fisherman's Friends song John in the Barrel....

لوك تشادويك

هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (يناير 2019) لوك تشادويك معلومات شخصية الميلاد 18 نوفمبر 1980 (العمر 43 سنة)كامبريدج الطول 5 قدم 11 بوصة (1.80 م) مركز اللعب وسط الجنسية المملكة المتحدة المدرسة ...

HCESAR

Portuguese keyboard layout HCESAR keyboard layout HCESAR typewriter Inverted vowel diagram HCESAR ([ɐˈɣa ˈsɛzaɾ]) is a Portuguese typewriter keyboard layout that takes its name from the first six letters on the first row of alphabetical keys: H C E S A R. Created by decree of the Estado Novo regime[1] on July 17, 1937, the layout placed the most frequently used keys in Portuguese in the center of the layout. The keys for vowels are positioned according to an inverted vow...

Military history of Italy

Part of a series on the History of Italy Early Prehistoric Italy Nuragic civilization (18th–3rd c. BC) Etruscan civilization (12th–6th c. BC) Magna Graecia (8th–3rd c. BC) Ancient Rome Kingdom (753 BC–509 BC) Republic (509 BC–27 BC) Roman expansion in Italy Roman Italy Populares and Optimates Empire (27 BC–286 AD) Western Empire (286 AD–476 AD) Praetorian prefecture of Italy Romano-Barbarian Kingdoms Odoacer's 476–493 Ostrogothic 493–553 ...

PROFILPELAJAR.COM