On a Beurling-Arveson Type Theorem for Some Functional Hilbert Spaces and Related Questions

2008 ◽  
Vol 62 (1) ◽  
pp. 77-84 ◽  
Author(s):  
M. T. Karaev
Keyword(s):  
Hilbert Spaces ◽  
Type Theorem ◽  
Functional Hilbert Spaces

scholarly journals Weighted composition operators on functional Hilbert spaces

1985 ◽  
Vol 31 (1) ◽  
pp. 117-126 ◽  
Author(s):  
R.K. Singh ◽  
R. David Chandra Kumar
Keyword(s):  
Hilbert Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Linear Operators ◽  
Weighted Composition Operators ◽  
Bounded Linear ◽  
Atomic Measure ◽  
Weighted Composition ◽  
Functional Hilbert Spaces

Let X be a non-empty set and let H(X) denote a Hibert space of complex-valued functions on X. Let T be a mapping from X to X and θ a mapping from X to C such that for all f in H(X), f ° T is in H(x) and the mappings CT taking f to f ° T and M taking f to θ.f are bounded linear operators on H(X). Then the operator CTMθ is called a weighted composition operator on H(X). This note is a report on the characterization of weighted composition operators on functional Hilbert spaces and the computation of the adjoint of such operators on L2 of an atomic measure space. Also the Fredholm criteria are discussed for such classes of operators.

scholarly journals Hilbert spaces have the Banach-Stone property for Bochner spaces

1983 ◽  
Vol 27 (1) ◽  
pp. 121-128 ◽  
Author(s):  
Peter Greim
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Type Theorem ◽  
Finite Measure ◽  
Linear Isometry ◽  
Measure Spaces ◽  
Stone Type ◽  
Stone Property

Let (ωi, σi, μi.) be two positive finite measure spaces, V a non-zero Hilbert space, and 1 ≤ p < ∞, p # 2. In this article it is shown that each surjective linear isometry between the Bochner spaces induces a Boolean isomorphism between the measure algebras , thus generalizing a result of Cambern's for separable Hilbert spaces.This Banach–Stone type theorem is achieved via a description of the Lp-structure of .

scholarly journals The subdifferential of the sum of two functions in Banach spaces II. Second order case

1995 ◽  
Vol 51 (2) ◽  
pp. 235-248 ◽  
Author(s):  
Robert Deville ◽  
El Mahjoub El Haddad
Keyword(s):  
Hilbert Spaces ◽  
Type Theorem ◽  
Continuous Functions ◽  
Second Order ◽  
Infinite Dimensional ◽  
Jacobi Operators ◽  
Uniqueness Results ◽  
Lower Semi ◽  
Order Case ◽  
Jacobi Equations

We prove a formula for the second order subdifferential of the sum of two lower semi continuous functions in finite dimensions. This formula yields an Alexandrov type theorem for continuous functions. We derive from this uniqueness results of viscosity solutions of second order Hamilton-Jacobi equations and singlevaluedness of the associated Hamilton-Jacobi operators. We also provide conterexamples in infinite dimensional Hilbert spaces.

scholarly journals Non-compact composition operators

1980 ◽  
Vol 21 (1) ◽  
pp. 125-130 ◽  
Author(s):  
R.K. Singh ◽  
S.D. Sharma
Keyword(s):  
Hilbert Spaces ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Functional Hilbert Spaces

In this note sufficient conditions for non-compactness of composition operators on two different functional Hilbert spaces have been obtained.

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