TY - CHAP

T1 - Maximality. Properties (B) and (C)

AU - Rubshtein, Ben Zion A.

AU - Grabarnik, Genady Ya

AU - Muratov, Mustafa A.

AU - Pashkova, Yulia S.

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

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.

UR - http://www.scopus.com/inward/record.url?scp=85006300283&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42758-4_8

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

M3 - Chapter

AN - SCOPUS:85006300283

T3 - Developments in Mathematics

SP - 95

EP - 110

BT - Developments in Mathematics

PB - Springer New York LLC

ER -