Juan Martínez

University of Granada | UGR · Department of Mathematical Analysis

An element x in the closed unit ball of a Banach space X is said to be geometrically compact (resp., geometrically weakly compact) if the set cp(2) ({x}) of all its second contractive perturbations is norm-compact (respectively, weakly compact). We say that x has finite geometric rank if the closed linear subspace generated by cp(2) ({x}) is finite...

We study orthogonality preserving operators between C∗-algebras, JB∗-algebras and JB∗-triples. Let be an orthogonality preserving bounded linear operator from a C∗-algebra to a JB∗-triple satisfying that T∗∗(1)=d is a von Neumann regular element. Then , every element in T(A) and d operator commute in the JB∗-algebra , and there exists a triple homo...

A theorem of Lusin is proved in the non-ordered context of JB*-triples. This is applied to obtain versions of a general transitivity theorem and to deduce refinements of facial structure in closed unit ballls of JB*-triples and duals.

We establish a geometric characterization of tripotents in real and complex JB * -triples. As a con-sequence we obtain an alternative proof of Kaup's Banach–Stone theorem for JB * -triples.  2004 Elsevier Inc. All rights reserved.

At the regional conference held at the University of California, Irvine, in 1985 [24], Harald Upmeier posed three basic questions regarding derivations on JB*-triples: (1) Are derivations automatically bounded? (2) When are all bounded derivations inner? (3) Can bounded derivations be approximated by inner derivations? These three questions had all...

We prove that, if E is a real JB*-triple having a predual then is the unique predual of E and the triple product on E is separately s(E,E*)-\sigma (E,E_{*_{}})-continuous.

We show that the set of all inner derivations of an ultraprime real Banach algebra is closed within all bounded derivations. More concretely, we show that for such an algebra A there exists a positive number γ (depending only on the “constant of ultraprimeness” of A) satisfying γ ∥ a+Z(A) ∥≦∥ D a ∥ for all a in A, where Z(A) denotes the centre of...

The concept of a Hilbert module (over an H * -algebra) arises as a generalization of that of a complex Hilbert space when the complex field is replaced by an (associative) H * -algebra with zero annihilator. P. P. Saworotnow [13] introduced Hilbert modules and extended to its context some classical theorems from the theory of Hilbert spaces, J. F....

We introduce the concept of tracial element for a nonassociative H * - algebra A with zero annihilator which extends the analogous one for associative H * -algebras by Saworotnow and Friedell. We show that the set of tracial elements enjoys many of the properties of the associative case. The canonical associative bilineal form on A given by 〈a,b〉:=...

JOURNAL OF ALGEBRA 147, 19-62 (1992) Structurable H*-Algebras M. CABRERA, J. MARTINEZ, AND A. RODRIGUEZ Deparlamento de Ancilisis Matembirico, Facultad de Ciencias, Unioersidad de Granada, 18071~Granada, Spain Communicated by Narhan Jacobson Received February 5, 1990 INTRODUCTION Structurable algebras were introduced by B. N. Allison in [ 11, where...

Complex (associative) H*-algebras were introduced and studied in detail by Ambrose[1]; it was proved that every complex H*-algebra with zero annihilator is the l2-sum of a suitable family of topologically simple complex H*-algebras and that the H*-algebras (H) of all Hilbert-Schmidt operators on any complex Hilbert space H are the only topologicall...

We prove that, if A denotes a topologically simple real (non-associative) H*-algebra, then either A is a topologically simple complex H*-algebra regarded as real H*-algebra or there is a topologically simple complex H*-algebra B with *-involution t such that A = {b Î B : t(b) = b*}. Using this, we obtain our main result, namely: (algebraically) iso...

The only finite-dimensional simple non-Lie Mal'cev complex algebra is given the structure of an H*-algebra and it is proved that this is the only topologically simple non-Lie Mal'cev H*-algebra.

If a is an element of a complex unital Banach algebra whose numerical range is confined to a closed angular region with vertex at zero and angle strictly less than π, we imbed a in a holomorphic semigroup with parameter in the open right half plane. There has been recently a great development in the theory of semigroups in Banach algebras (see [6])...