Chebyshev’s inequality for Banach-space-valued random elements

The Davis-gut Law for Independent and Identically Distributed Banach Space Valued Random Elements

Central Limit Theorem for Banach Space Valued Fuzzy Random Variables

In this paper we prove a central limit theorem for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.

Hölder Versions of Banach Space Valued Random Fields

For rather general moduli of smoothness ρ, like ρ(h)=h ln(c/h), we consider the Hölder spaces Hρ(B) of functions [0, 1] → B where B is a separable Banach space. We establish an isomorphism between Hρ(B) and some sequence Banach space. With this analytical tool, we follow a very natural way to study, in terms of second differences, the existence of a version in Hρ(B) for a given random field. 20...

Higher Moments of Banach Space Valued Random Variables

We define the k:th moment of a Banach space valued random variable as the expectation of its k:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. We study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals...

On the character space of Banach vector-valued function algebras

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...