Operator and Dual Operator Bases in Linear Topological Spaces

Operator-valued bases on Hilbert spaces

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

Dual Generalized Bases in Linear Topological Spaces

Operator Algebras and Dual Spaces

1. An isomorphism theorem. In this paper we discuss a particular method of introducing a convolution product into certain topological linear spaces so that they become algebras. The space in each case will be essentially the dual space of a linear space of continuous functions, and arises in the study of general group algebras and in the theory of distributions. Let G be a topological group, wr...

operator-valued bases on hilbert spaces

in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also dene the concepts of bessel, hilbert ov-basis and obt...

Shift-Invariant Spaces and Linear Operator Equations

In this paper we investigate the structure of finitely generated shift-invariant spaces and solvability of linear operator equations. Fourier transforms and semi-convolutions are used to characterize shift-invariant spaces. Criteria are provided for solvability of linear operator equations, including linear partial difference equations and discrete convolution equations. The results are then ap...