Wyniki wyszukiwania

1

Multipliers and Wiener-Hopf operators on weighted L p spaces

100%

Petkova V.

Open Mathematics

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2013

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tom 11

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nr 3

561-573

EN

We study multipliers M (bounded operators commuting with translations) on weighted spaces L ω p (ℝ), and establish the existence of a symbol µM for M, and some spectral results for translations S t and multipliers. We also study operators T on the weighted space L ω p (ℝ+) commuting either with the right translations S t , t ∈ ℝ+, or left translations P +S −t , t ∈ ℝ+, and establish the existence of a symbol µ of T. We characterize completely the spectrum σ(S t ) of the operator S t proving that $\sigma (S_t ) = \{ z \in \mathbb{C}:|z| \leqslant e^{t\alpha _0 } \} ,$ where α 0 is the growth bound of (S t )t≥0. A similar result is obtained for the spectrum of (P +S −t ), t ≥ 0. Moreover, for an operator T commuting with S t , t ≥ 0, we establish the inclusion [...] , where $\mathcal{O}$ = {z ∈ ℂ: Im z α 0}.

2

An overview of some recent developments on the Invariant Subspace Problem

64%

Chalendar I., Partington J. R.

Concrete Operators

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2013

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tom 1

1-10

EN

This paper presents an account of some recent approaches to the Invariant Subspace Problem. It contains a brief historical account of the problem, and some more detailed discussions of specific topics, namely, universal operators, the Bishop operators, and Read’s Banach space counter-example involving a finitely strictly singular operator.

3

Superposition operator on the space of sequences almost converging to zero

64%

Alekhno E.

Open Mathematics

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2012

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tom 10

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nr 2

619-645

EN

We study the superposition operator f on on the space ac 0 of sequences almost converging to zero. Conditions are derived for which f has a representation of the form f x = a+bx +g x, for all x ∈ ac 0 with a = f 0, b ∈ D(ac 0), g a superposition operator from ℓ∞ into I(ac 0), D(ac 0) = {z: zx ∈ ac 0 for all x ∈ ac 0}, and I(ac 0) the maximal ideal in ac 0. If f is generated by a function f of a real variable, then f is linear. We consider the conditions for which a bounded function f generates f acting on ac 0 and the conditions for which there exists a sequence y ∈ ac 0 such that y − f y ∈ ac 0. In terms of f, criteria for the boundedness, continuity, and sequential σ(ac 0ℓ1)-continuity of f on ac 0 are given. It is shown that the continuity of f is equivalent to the weak sequential continuity. Finally, properties of spaces D(ac 0) and I(ac 0) are studied, and in particular it is established that the inclusion I(ac 0) ⊕ {λe: λ ∈ ℝ} ⊂ D(ac 0) is proper, where e = (1, 1, …). By means of D(ac 0), a number of Banach-Mazur limit properties are derived.

4

Unbounded Hermitian operators and relative reproducing kernel Hilbert space

52%

Jorgensen P.

Open Mathematics

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2010

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tom 8

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nr 3

569-596

EN

We study unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we identify additional structures that throw light on the problem. We will attack the problem of computing deficiency spaces for a single Hermitian operator with dense domain in a Hilbert space which occurs in a duality relation with a second Hermitian operator, often in the same Hilbert space.

Ograniczanie wyników

3 Open Mathematics

1 Concrete Operators

1 Alekhno E.

1 Chalendar I.

1 Jorgensen P.

1 Partington J. R.

1 Petkova V.

1 2013

2 2012

1 2010

Multipliers and Wiener-Hopf operators on weighted L p spaces

An overview of some recent developments on the Invariant Subspace Problem

Superposition operator on the space of sequences almost converging to zero

Unbounded Hermitian operators and relative reproducing kernel Hilbert space