Subdifferentiability of the norm and the Banach-Stone Theorem for real and complex JB∗-triples
نویسندگان
چکیده
We study the points of strong subdifferentiability for the norm of a real JB∗-triple. As a consequence we describe weakly compact real JB∗-triples and rediscover the Banach-Stone Theorem for complex JB∗-triples.
منابع مشابه
Embedding normed linear spaces into $C(X)$
It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can ...
متن کامل$(-1)$-Weak Amenability of Second Dual of Real Banach Algebras
Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on $ A_mathbb{C} $ satisfying a simple condition together with the norm $ | cdot | $ on $ A$. In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...
متن کاملOn the axiomatic definition of real JB∗–triples
In the last twenty years, a theory of real Jordan triples has been developed. In 1994 T. Dang and B. Russo introduced the concept of J∗B–triple. These J∗B–triples include real C∗–algebras and complex JB∗–triples. However, concerning J∗B–triples, an important problem was left open. Indeed, the question was whether the complexification of a J∗B–triple is a complex JB∗–triple in some norm extendin...
متن کاملStrong convergence theorem for finite family of m-accretive operators in Banach spaces
The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.
متن کاملBounded symmetric domains and generalized operator algebras
Jordan C*-algebras go back to Kaplansky, see [20]. Let J be a complex Banach Jordan algebra, that is, a complex Banach space with commutative bilinear product x◦y satisfying x◦(x2◦y) = x2◦(x◦y) as well as ||x◦y|| ≤ ||x||·||y||, Bounded symmetric domains and generalized operator algebras 51 and suppose that on J is given a (conjugate linear) isometric algebra involution x 7→ x∗. Then J is called...
متن کامل