Multiplication operators on Hilbert spaces of analytic functions

Yousefi, B.

doi:10.1007/s00013-004-1040-0

Cited by 17 publications

(5 citation statements)

References 4 publications

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“…In the rest of the paper we assume that X is a Banach space of analytic functions on the open unit disc U satisfying the conditions that come in the introduction. For some works on these topics see [1][2][3][4][5][6][7]. Assume, further that the composition operators C aϕ are bounded and invertible on X where ϕ is a multiplier of X and 0 < |a| ≤ 1.…”

Section: Resultsmentioning

confidence: 99%

Intertwining operators on Banach function spaces

Yousefi¹,

Doroodgar²

2007

imf

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Section: Resultsmentioning

confidence: 99%

Intertwining operators on Banach function spaces

Yousefi¹,

Doroodgar²

2007

imf

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“…Let Y =  (U)  and Z =  , then Y and Z are quasi-affinities intertwining T and M  U  T 1  T 2 and satisfying ZY = (M) and ZY = (T) c.f. [16] theorem 2.1) [17]. For K  Lat T. The mappings K  and L  L preserve the lattice operations in Lat T and Lat M and are inverse to each other.…”

Section: Theoremmentioning

confidence: 99%

On Reflexivity of Certain Hyponormal Operators with Double Commutant Property

Kothiyal¹

2021

JAMCS

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Sarason did pioneer work on the reflexivity and purpose of this paper is to discuss the reflexivity of different class of contractions. Among contractions it is now known that C11 contractions with finite defect indices, C.o contractions with unequal defect indices and C1. contractions with at least one finite defect indices are reflexive. More over the characterization of reflexive operators among co contractions and completely non unitary weak contractions with finite defect indices has been reduced to that of S (F), the compression of the shift on H2 ⊖ F H2, F is inner. The present work is mainly focused on the reflexivity of contractions whose characteristic function is constant. This class of operator include many other isometries, co-isometries and their direct sum. We shall also discuss the reflexivity of hyponormal contractions, reflexivity of C1. contractions and weak contractions. It is already known that normal operators isometries, quasinormal and sub-normal operators are reflexive. We partially generalize these results by showing that certain hyponormal operators with double commutant property are reflexive. In addition, reflexivity of operators which are direct sum of a unitary operator and C.o contractions with unequal defect indices,is proved Each of this kind of operator is reflexive and satisfies the double commutant property with some restrictions.

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“…In [26] it is shown that any powers of the operator M z is reflexive on Banach spaces of formal Laurent series. Also, reflexivity of the multiplication operators on some function spaces has been investigated in [6,10,11,20,24,27]. In this article we would like to give some sufficient conditions so that the powers of the operator M z , acting on Banach function spaces becomes reflexive.…”

Section: Introductionmentioning

confidence: 99%