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On a decomposition for pairs of commuting contractions

Zbigniew Burdak (2007)

Studia Mathematica

A new decomposition of a pair of commuting, but not necessarily doubly commuting contractions is proposed. In the case of power partial isometries a more detailed decomposition is given.

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

Zagorodniuk, S. (1998)

Serdica Mathematical Journal

∗ Partially supported by Grant MM-428/94 of MESC.Systems of orthogonal polynomials on the real line play an important role in the theory of special functions [1]. They find applications in numerous problems of mathematical physics and classical analysis. It is known, that classical polynomials have a number of properties, which uniquely define them.

On a fixed-point theorem of Cellina

Stephen Simons (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota mostriamo come un teorema di esistenza per funzionali lineari porti un nuovo teorema di punto fisso che generalizza un teorema di punto fisso di Cellina.

On a formula for the jumps in the semi-Fredholm domain.

Vladimir Rakocevic (1992)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we prove some properties of the lower s-numbers and derive asymptotic formulae for the jumps in the semi-Fredholm domain of a bounded linear operator on a Banach space.

On a general bidimensional extrapolation problem

Rodrigo Arocena, Fernando Montana (1993)

Colloquium Mathematicae

Several generalized moment problems in two dimensions are particular cases of the general problem of giving conditions that ensure that two isometries, with domains and ranges contained in the same Hilbert space, have commutative unitary extensions to a space that contains the given one. Some results concerning this problem are presented and applied to the extension of functions of positive type.

On a generalization of Lumer-Phillips' theorem for dissipative operators in a Banach space

Driss Drissi (1998)

Studia Mathematica

Using [1], which is a local generalization of Gelfand's result for powerbounded operators, we first give a quantitative local extension of Lumer-Philips' result that states conditions under which a quasi-nilpotent dissipative operator vanishes. Secondly, we also improve Lumer-Phillips' theorem on strongly continuous semigroups of contraction operators.

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