Abstract We prove that for a Banach algebra A having bounded $\mathcal {Z}(A)$ -approximate identity and every $\mathbf {[IN]}$ group G with weight w which is either constant on conjugacy classes or satisfies $w \geq 1$ , {Z}(L^{1}_{w}(G) \otimes ^{\gamma } A) \cong \mathcal {Z}(L^{1}_{w}(G)) . As an application, we discuss the conditions under {Z}(L^{1}_{\omega }(G,A))$ enjoys certain algebrai...

In this paper, we have studied the Henstock - Kurzweil integral which is a generalized Riemann means. Hen-stock natural extension of integral. We defined Banach space valued function with respect to bounded variation an real increasing function. investigated elementary properties variation. proved convergence theorems and Saks lemma functions vari-ation. Equi-integrability equi-integrable theor...

The Hölder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extended real-valued functions of two variables. A classification scheme for the general Hölder metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal...

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...

We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral polynomials: they do not always extend to X-valued Grothendieck-integral polynomials. However, they...

We use Baire categorical arguments to construct dramatically pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that \almost every continuous real-valued function deened on 0,1] is nowhere diierentiable". As with the results of Banach and Mazurkiewicz, it appears...

We propose a definition of admissible Dirichlet series as the analog of Hayman’s [6] 1956 definition of admissible power series.