Related papers: Generalizing the Paley-Wiener perturbation theory …
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 provide sufficient conditions for a mapping between two Banach spaces to be a diffeomorphism using the approach of an auxiliary functional and also by the aid of a duality mapping corresponding to a normalization function. We simplify…
I introduce Banach spaces on which it is possible to precisely characterize the spectrum of the transfer operator associated to a piecewise expanding map with H\"older weight.
We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and $C^1$ functions. This way we prove more directly a result by Lee and Naor and we generalize the $C^1$…
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued…
We introduce the notions of tauberian, cotauberian and weakly compact pair of closed subspaces of a Banach space. The theory produced by these notions is richer than that of the corresponding operators since an operator can be regarded as a…
The celebrated Paley-Wiener theorem naturally identifies the spaces of bandlimited functions with subspaces of entire functions of exponential type. Recently, it has been shown that these spaces remain invariant only under composition with…
We review recent work connected with the invariant subspace problem for operators, in particular new developments in the last 15 years. In particular, we include discussions of almost-invariant subspaces, universal operators, specific…
We present some results related to Hahn-Banach extension theorem for linear operators on asymmetric normed spaces. L. Nachbin, Trans. Amer. Math. Soc. 68 (1950), proved that a Banach space has the extension property for linear operators (a…
The notion of linear Hahn-Banach extension operator was first studied in detail by Heinrich and Mankiewicz (1982). Previously, J. Lindenstrauss (1966) studied similar versions of this notion in the context of non separable reflexive Banach…
We introduce the notion of subprojective and superprojective operators and we use them to prove a variation of the three-space property for subprojective and superprojective spaces. As an application, we show that some spaces considered by…
This paper is an account (without proofs) of the results of our work "Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications", funct-an/9311001. The Section 9 establishing a connection between variational…
We use the injective envelope to study quasimultipliers of operator spaces. We prove that all representable operator algebra products that an operator space can be endowed with are induced by quasimultipliers. We obtain generalizations of…
We construct a nonexpansive linear operator on the Gurarii space that "captures" all nonexpansive linear operators between separable Banach spaces. Some additional properties involving its restrictions to finite-dimensional subspaces…
We prove a generalisation of Fernique's theorem which applies to a class of (measurable) functionals on abstract Wiener spaces by using the isoperimetric inequality. Our motivation comes from rough path theory where one deals with iterated…
It is shown that certain lower semi-continuous maps from a paracompact space to the family of closed subsets of the bundle space of a Banach bundle admit continuous selections. This generalization of the theorem of Douady, dal…
The classical results on oversampling and undersampling (or aliasing), of functions in Paley-Wiener spaces, are generalized to the case of functions in de Branges spaces arising from regular Schr\"odinger operators with a wide range of…
This paper explores Paley-Wiener type theorems within the framework of hypercomplex variables. The investigation focuses on a space-fractional version of the Dirac operator $\mathbf{D}_\theta^{\alpha}$ of order $\alpha$ and skewness…
The notion of decomposable operators acting between distinct $L^p$-direct integrals of Banach spaces is introduced. We show that these operators generalize the composition operator, in sense that a mapping is replaced by a binary relation.…
After different variables and functions changes, the generalized dispersal problem, recalled in (1) below and considered in part I, see [14], leads us to invert a sum of linear operators in a suitable Banach space, see (2) below. The…