The bounded approximation property for weakly uniformly continuous type holomorphic mappings.
The category of disintegration
The Cauchy-Riemann equations in infinite dimensions
I will explain basic concepts/problems of complex analysis in infinite dimensions, and survey the few approaches that are available to solve those problems.
The Cauchy-Riemann operator in infinite dimensional spaces.
The Daugavet equation for polynomials
We study when the Daugavet equation is satisfied for weakly compact polynomials on a Banach space X, i.e. when the equality ||Id + P|| = 1 + ||P|| is satisfied for all weakly compact polynomials P: X → X. We show that this is the case when X = C(K), the real or complex space of continuous functions on a compact space K without isolated points. We also study the alternative Daugavet equation for polynomials P: X → X. We show that this equation holds for every polynomial on the complex space X =...
The density property for JB*-triples
We obtain conditions on a JB*-algebra X so that the canonical embedding of X into its associated quasi-invertible manifold has dense range. We prove that if a JB* has this density property then the quasi-invertible manifold is homogeneous for biholomorphic mappings. Explicit formulae for the biholomorphic mappings are also given.
The dual of every Asplund space admits a projectional resolution of the identity
The Ekeland's variational principle for vector-valued multifunctions.
The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of -algebras
The aim of this paper is to start a systematic investigation of the existence of angular limits and angular derivatives of holomorphic maps of infinite dimensional Siegel domains in -algebras. Since -algebras are natural generalizations of -algebras, -algebras, -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.
The Feynman integral and Feynman's operational calculus: a heuristic and mathematical introduction
The fixed points of holomorphic maps on a convex domain
We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.
The general Fubini theorem in complete bornological locally convex spaces.
The Graves theorem revisited.
The Kluvanek-Kantorovitz characterization of scalar operators in locally convex spaces.
The Laplace transform of exponentially bounded vector-valued functions (real conditions)
The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition
It is proved that the Levi problem for certain locally convex Hausdorff spaces over with a finite dimensional Schauder decomposition (for example for Fréchet or Silva spaces with a Schauder basis) the Levi problem has a solution, i.e. every pseudoconvex domain spread over is a domain of existence of an analytic function. It is also shown that a pseudoconvex domain spread over a Fréchet space or a Silva space with a finite dimensional Schauder decomposition is holomorphically convex and satisfies...
The Levi problem in non-locally convex seperable topological vector spaces.
The McShane, PU and Henstock integrals of Banach valued functions
Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals...
The multiplier for the weak McShane integral
The multiplier for the weak McShane integral which has been introduced by M. Saadoune and R. Sayyad (2014) is characterized.
The Nikodym theorems for operator measures.