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Functional calculus for a class of unbounded linear operators on some non-archimedean Banach spaces

Dodzi Attimu, Toka Diagana (2009)

Commentationes Mathematicae Universitatis Carolinae

This paper is mainly concerned with extensions of the so-called Vishik functional calculus for analytic bounded linear operators to a class of unbounded linear operators on c 0 . For that, our first task consists of introducing a new class of linear operators denoted W ( c 0 ( J , ω , 𝕂 ) ) and next we make extensive use of such a new class along with the concept of convergence in the sense of resolvents to construct a functional calculus for a large class of unbounded linear operators.

Functional models and asymptotically orthonormal sequences

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2003)

Annales de l’institut Fourier

Suppose H 2 is the Hardy space of the unit disc in the complex plane, while Θ is an inner function. We give conditions for a sequence of normalized reproducing kernels in the model space K Θ = H 2 ⊖ Θ H 2 to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.

Functions of bounded variation on compact subsets of the plane

Brenden Ashton, Ian Doust (2005)

Studia Mathematica

A major obstacle in extending the theory of well-bounded operators to cover operators whose spectrum is not necessarily real has been the lack of a suitable variation norm applicable to functions defined on an arbitrary nonempty compact subset σ of the plane. In this paper we define a new Banach algebra BV(σ) of functions of bounded variation on such a set and show that the function-theoretic properties of this algebra make it better suited to applications in spectral theory than those used previously....

Functions of operators and their commutators in perturbation theory

Yu. Farforovskaya (1994)

Banach Center Publications

This paper shows some directions of perturbation theory for Lipschitz functions of selfadjoint and normal operators, without giving precise proofs. Some of the ideas discussed are explained informally or for the finite-dimensional case. Several unsolved problems are mentioned.

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