1996
DOI: 10.1112/blms/28.2.156
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Smoothness Properties of the Unit Ball in a JB* -Triple

Abstract: An element a of norm one in a JB*-triple A is said to be smooth if there exists a unique element x in the unit ball A* of the dual A* of A at which a attains its norm, and is said to be Frechet-smooth if, in addition, any sequence (x n ) of elements in A* for which (x n (a)) converges to one necessarily converges in norm to x. The sequence (a 2n+1 ) of odd powers of a converges in the weak*-topology to a tripotent u(a) in the JBW*-envelope A** of A. It is shown that a is smooth if and only if u(a) is a minimal… Show more

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Cited by 5 publications
(4 citation statements)
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“…With respect to the separately weak à -continuous product aY b U 3 a b fa u bg and the norm-preserving involution a U 3 a y fu a ug, A 2 u is a JBW à -algebra with unit u. For details the reader is referred to [1], [3], [4], [5], [7], [10], [12], [13], [14], [15], [16], [17], [19], [20], [23].…”
Section: Preliminariesmentioning
confidence: 99%
“…With respect to the separately weak à -continuous product aY b U 3 a b fa u bg and the norm-preserving involution a U 3 a y fu a ug, A 2 u is a JBW à -algebra with unit u. For details the reader is referred to [1], [3], [4], [5], [7], [10], [12], [13], [14], [15], [16], [17], [19], [20], [23].…”
Section: Preliminariesmentioning
confidence: 99%
“…The following corollary is an extension to real JB * -triples of the main result of [10] for complex JB * -triples. Corollary 2.6.…”
Section: Resultsmentioning
confidence: 99%
“…Identification of smooth points of spaces of operators , C * -algebras and their generalizations has received a lot of attention in the literature. See [H,GY1,GY2,KY,MR,TW,W1,W2,HWW] Chapter VI. Motivated by these results, in this paper we study very smooth points of spaces of operators and JB * -triples.…”
Section: Introductionmentioning
confidence: 99%