Maximality. Properties (B) and (C)

Ben Zion A. Rubshtein; Genady Ya Grabarnik; Mustafa A. Muratov; Yulia S. Pashkova

doi:10.1007/978-3-319-42758-4_8

Maximality. Properties (B) and (C)

Ben Zion A. Rubshtein, Genady Ya Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

In this chapter, we study the second associate space X¹¹ of a symmetric space X. To describe properties of the natural embedding X ⊆ X¹¹, we two consider important properties (B) and (C) of the space X. We show that X has property (C) if and only if the natural embedding X ⟶ X¹¹ is isometric. If in addition to (C), X has property (B), then X = X¹¹, i.e., the symmetric space X is maximal, and the natural embedding X ⟶ X¹¹ is an isometric isomorphism between X and X¹¹.

Original language	English
Title of host publication	Developments in Mathematics
Publisher	Springer New York LLC
Pages	95-110
Number of pages	16
DOIs	https://doi.org/10.1007/978-3-319-42758-4_8
State	Published - 1 Jan 2016

Publication series

Name	Developments in Mathematics
Volume	45
ISSN (Print)	1389-2177

ASJC Scopus subject areas

General Mathematics

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10.1007/978-3-319-42758-4_8

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title = "Maximality. Properties (B) and (C)",

abstract = "In this chapter, we study the second associate space X11 of a symmetric space X. To describe properties of the natural embedding X ⊆ X11, we two consider important properties (B) and (C) of the space X. We show that X has property (C) if and only if the natural embedding X ⟶ X11 is isometric. If in addition to (C), X has property (B), then X = X11, i.e., the symmetric space X is maximal, and the natural embedding X ⟶ X11 is an isometric isomorphism between X and X11.",

author = "Rubshtein, {Ben Zion A.} and Grabarnik, {Genady Ya} and Muratov, {Mustafa A.} and Pashkova, {Yulia S.}",

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AU - Grabarnik, Genady Ya

AU - Muratov, Mustafa A.

AU - Pashkova, Yulia S.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this chapter, we study the second associate space X11 of a symmetric space X. To describe properties of the natural embedding X ⊆ X11, we two consider important properties (B) and (C) of the space X. We show that X has property (C) if and only if the natural embedding X ⟶ X11 is isometric. If in addition to (C), X has property (B), then X = X11, i.e., the symmetric space X is maximal, and the natural embedding X ⟶ X11 is an isometric isomorphism between X and X11.

AB - In this chapter, we study the second associate space X11 of a symmetric space X. To describe properties of the natural embedding X ⊆ X11, we two consider important properties (B) and (C) of the space X. We show that X has property (C) if and only if the natural embedding X ⟶ X11 is isometric. If in addition to (C), X has property (B), then X = X11, i.e., the symmetric space X is maximal, and the natural embedding X ⟶ X11 is an isometric isomorphism between X and X11.

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BT - Developments in Mathematics

PB - Springer New York LLC

ER -

Maximality. Properties (B) and (C)

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