q-positive definiteness and related operators

Ôta, Schôichi; Szafraniec, Franciszek Hugon

doi:10.1016/j.jmaa.2006.07.006

Cited by 8 publications

(6 citation statements)

References 10 publications

(18 reference statements)

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“…The class of q-quasinormal operators, a particular case of q-deformed operators introduced byÔta in [13] (see also [14,16,17]) in connection with the theory of quantum groups (see [8]), is well-suited for our purposes.…”

Section: Remarks and Further Resultsmentioning

confidence: 99%

Operators with absolute continuity properties: an application to quasinormality

Jabłoński¹,

Jung²,

Stochel³

2013

Studia Math.

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Abstract. An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerged in this context are invented. Various examples and counterexamples illustrating the concepts of the paper are constructed by means of weighted shifts on directed trees. Generalizations of these results that cover the case of q-quasinormal operators are established.

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Section: Remarks and Further Resultsmentioning

confidence: 99%

Operators with absolute continuity properties: an application to quasinormality

Jabłoński¹,

Jung²,

Stochel³

2013

Studia Math.

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“…Operators satisfying the condition T T * = qT * T were introduced in [6]. They are called q-normal operators and have been studied in [4] and [7]. Now M θ and M θ are not necessarily adjoint operators in P G l,q .…”

Section: Corollary 22mentioning

confidence: 99%

Paragrassmann algebras as quantum spaces, Part II: Toeplitz Operators

Sontz¹

2014

J. Operator Theory

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This paper continues the study of paragrassmann algebras begun in Part I with the definition and analysis of Toeplitz operators in the associated holomorphic Segal-Bargmann space. These are defined in the usual way as multiplication by a symbol followed by the projection defined by the reproducing kernel. These are non-trivial examples of spaces with Toeplitz operators whose symbols are not functions and which themselves are not spaces of functions.MSC (2000): 46E22, 47B32, 47B35, 81R05

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“…We say that A is q-normal if A is q-formally normal and D(A) = D(A * ). We refer the reader to [17,18] for a treatment on q-normals and related classes of operators. Note that (a2) together with Ā0 = A * gives q-normality of Ā.…”

Section: Preliminariesmentioning

confidence: 99%