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Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization
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A. R. Soltani
Veröffentlicht/Copyright:
24. Februar 2010
Abstract
Let X and Y be two Hilbert spaces, and 
the space of bounded linear transformations from X into Y. Let {An} ⊂ be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (Spectral theory of periodically and quasi-periodically stationary SαS sequences, University of North Carolina, Chapel Hill, 1991). In this work we proceed further to characterize {An} by a positive measure μ and a number T of 
-valued functions a0, . . . , aT–1; in the spectral form 
, where 
and Φ is an -valued Borel set function on [0, 2π) such that
(Φ(Δ)x, Φ(Δ′)x′)Y = (x, x′)X μ(Δ ∩ Δ′).
Key words and phrases.: Hilbert space; bounded linear operators; weakly periodic sequences; spectral representation
Received: 1996-12-18
Revised: 1997-09-05
Published Online: 2010-02-24
Published in Print: 1999-February
© 1999 Plenum Publishing Corporation
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- Tensor Products of Non-Archimedean Weighted Spaces of Continuous Functions
- On Periodic Solutions of Nonlinear Functional Differential Equations
- Two-Weighted Inequalities for Integral Operators in Lorentz Spaces Defined on Homogeneous Groups
- On the Absolute Summability of Series with Respect to Block-Orthonormal Systems
- Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization
Schlagwörter für diesen Artikel
Hilbert space;
bounded linear operators;
weakly periodic sequences;
spectral representation
Artikel in diesem Heft
- Application of Analogues of General Kolosov–Muskhelishvili Representations in the Theory of Elastic Mixtures
- A Radial Derivative with Boundary Values of the Spherical Poisson Integral
- Tensor Products of Non-Archimedean Weighted Spaces of Continuous Functions
- On Periodic Solutions of Nonlinear Functional Differential Equations
- Two-Weighted Inequalities for Integral Operators in Lorentz Spaces Defined on Homogeneous Groups
- On the Absolute Summability of Series with Respect to Block-Orthonormal Systems
- Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization
