Pick-nevanlinna interpolation theorem and multiplication operators on functional Hilbert spaces

1991 ◽  
Vol 14 (6) ◽  
pp. 825-836 ◽  
Author(s):  
Gadadhar Misra
Keyword(s):  
Hilbert Spaces ◽  
Interpolation Theorem ◽  
Multiplication Operators ◽  
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 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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