Related papers: Product spaces generated by bilinear maps and dual…
For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. This is used to produce spaces with a small amount of structure. We present…
We develop a systematic approach to the study of duality for ideals of Lipschitz maps from a metric space to a Banach space, inspired by the classical theory that relates ideals of operators and tensor norms for Banach spaces, by using the…
We study the algebra of bilinear multiplications of an $n$-dimensional vector space. In particular, we study the Kantor product of some well-known (associative, Lie, alternative, Novikov and some other) multiplications.
We give a self contained introduction to A$_\infty$-algebras, A$_\infty$-bimodules and maps between them. The case of A$_\infty$-bimodule-map between $A$ and its dual space $A^{*}$, which we call $\infty$-inner-product, will be investigated…
In this paper we discuss symmetrically self-dual spaces, which are simply real vector spaces with a symmetric bilinear form. Certain subsets of the space will be called q-positive, where q is the quadratic form induced by the original…
We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are…
We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…
Let $A$ and $B$ be Banach algebras and let $B$ be an algebraic Banach $A-$bimodule. Then the $\ell^1-$direct sum $A\times B$ equipped with the multiplication $$(a_1,b_1)(a_2,b_2)=(a_1a_2,a_1\cdot b_2+b_1\cdot a_2+b_1b_2),~~ (a_1, a_2\in A,…
We develop a duality theory for multiplier Banach-Hopf algebras over a non-Archimedean field K. As examples, we consider algebras corresponding to discrete groups and zero-dimensional locally compact groups with K-valued Haar measure, as…
We answer in the affirmative the surprisingly difficult questions: If a complex Banach space possesses a real predual X, then is X a complex Banach space? If a complex Banach space possesses a real predual, then does it have a complex…
We characterize all entire functions that transform a weighted Banach spaces of analytic functions $\mathcal{H}^{\infty}_{\mu_1}$ into another space of the same kind $\mathcal{H}^{\infty}_{\mu_2}$ by superposition for very general weights…
We introduce the operators "modified limit" and "accumulation" on a Banach space, and we use this to define what we mean by being internally computable over the space. We prove that any externally computable function from a computable…
In the literature surrounding the theory of Banach spaces, considerable effort has been invested in exploring the conditions on a Banach space X that characterise X as being an inner product space or as a linearly isomorphic copy of a…
We investigate the category of ``matricial order operator spaces,'' which generalize operator systems, being equipped with both matricial norms and matricial order. For these objects, we develop duality theory. Taking a cue from the theory…
We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples…
We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial construction (blocker duality) which yields…
A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are…
Representations of polynomial covariant type commutation relations by pairs of linear integral operators and multiplication operators on Banach spaces $L_p$ are constructed.
In this paper, we characterize the (left) multiplier algebra of a semidirect product algebra ${\mathcal A}={\mathcal B}\oplus {\mathcal I}$, where ${\mathcal I}$ and ${\mathcal B}$ are closed two-sided ideal and closed subalgebra of…
In this paper, the concept of selective real manifolds is extended. It is proved that the product of two selective Banach manifolds is a selective Banach manifold. The notion of the $\alpha$--level differentiation of the mappings between…