Let X be a Banach space and suppose that A1, . . . ,An are noncommuting (that is, not necessarily commuting) elements in L(X), the space of bounded linear operators on X. Further, for each i ∈ {1, . . . , n}, let μi be a continuous probability measure on B([0,1]), the Borel class of [0,1]. Each such n-tuple of operator-measure pairs (Ai,μi), i = 1, . . . , n, determines an operational calculus ...

We study non-linear traces of the Choquet type and Sugeno on algebra compact operators. They have certain partial additivities. show that these additivities characterize both respectively. There exists a close relation between majorization theory. trace class operators for type. More generally we discuss Schatten–von Neumann p-class determine when they form Banach spaces. This is an attempt at ...

in this paper, we study the arens regularity properties of module actions and we extend some proposition from baker, dales, lau and others into general situations. we establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. in 1951 arens shows that the second dual of banach algebra endowed with the e...

‎Let $X$‎, ‎$Y$ and $Z$ be Banach spaces and $f:Xtimes Y‎ ‎longrightarrow Z$ a bounded bilinear map‎. ‎In this paper we‎ ‎study the relation between Arens regularity of $f$ and the‎ ‎reflexivity of $Y$‎. ‎We also give some conditions under which the‎ ‎Arens regularity of a Banach algebra $A$ implies the Arens‎ ‎regularity of certain Banach right module action of $A$‎ .

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...

A survey is given of the work on strong regularity for uniform algebras over the last thirty years, and some new results are proved, including the following. Let A be a uniform algebra on a compact space X and let E be the set of all those points x ∈ X such that A is not strongly regular at x. If E has no non-empty, perfect subsets then A is normal, and X is the character space of A. If X is ei...

in a commutative noetherian local complex normed algebra which is complete in its m-adic metric there are only finitely many closed prime ideals.

We establish triviality of some holomorphic Banach vector bundles on the maximal ideal space M(H∞) of the Banach algebra H∞ of bounded holomorphic functions on the unit disk D ⊂ C with pointwise multiplication and supremum norm. We apply the result to the study of the Sz.-Nagy operator corona problem. 1. Formulation of Main Results 1.1. We continue our study started in [Br2] of analytic objects...