Examining Hyponormality of Sequence of Toeplitz Operators of Symbols on Bergman Spaces.

For a sequence of πœ‘π‘–π‘— in 𝐿 (πœ•π·) , let 𝑃𝑖𝑗𝑖 𝑗=1 𝑓𝑖𝑖=1𝑔𝑗𝑗=1 Where 𝑓𝑖 and 𝑔𝑗 are two corresponding sequences in 𝐻 . Inthis paper, it is shown that the Toeplitz operators π‘‡πœ‘π‘–π‘— arehyponormals if and only if π‘”π‘Ÿ 𝑐 π‘‡β„Žπ‘Ÿ π‘“π‘Ÿ for some constant c andsome functions β„Žπ‘Ÿ in 𝐻 (πœ•π·) with β„Žπ‘Ÿ ≀ for any π‘Ÿ .And, for a bounded analytic sequence πœ‘π‘–π‘— π‘œπ‘› 𝐷 , we show that asequence of a Toeplitz operator π‘‡πœ‘π‘–π‘— are analytic if πœ‘π‘–π‘— 𝑖𝑠 𝑖𝑛 𝐻 . Theseare easily seen to be subnormal:Where πΏπœ‘π‘–π‘— are normal operator of multiplication by πœ‘π‘–π‘— in 𝐿 (πœ•π·) .Lastly, for πœ‘π‘–π‘— ∈ 𝐿 we show that, the sequence of Toeplitz operatorπ‘‡πœ‘π‘–π‘— on the Bergman space with symbol πœ‘π‘–π‘— given by:are analytic if πœ‘π‘–π‘— ∈ 𝐻 .

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2024-12-11
DOI
https://doi.org/10.5281/zenodo.14381864
Primary Topic
Holomorphic and Operator Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

Examining Hyponormality of Sequence of Toeplitz Operators of Symbols on Bergman Spaces.

Zenodo (CERN European Organization for Nuclear Research)
Holomorphic and Operator Theory
article

Examining Hyponormality of Sequence of Toeplitz Operators of Symbols on Bergman Spaces.

article en

Abstract

For a sequence of πœ‘π‘–π‘— in 𝐿 (πœ•π·) , let 𝑃𝑖𝑗𝑖 𝑗=1 𝑓𝑖𝑖=1𝑔𝑗𝑗=1 Where 𝑓𝑖 and 𝑔𝑗 are two corresponding sequences in 𝐻 . Inthis paper, it is shown that the Toeplitz operators π‘‡πœ‘π‘–π‘— arehyponormals if and only if π‘”π‘Ÿ 𝑐 π‘‡β„Žπ‘Ÿ π‘“π‘Ÿ for some constant c andsome functions β„Žπ‘Ÿ in 𝐻 (πœ•π·) with β„Žπ‘Ÿ ≀ for any π‘Ÿ .And, for a bounded analytic sequence πœ‘π‘–π‘— π‘œπ‘› 𝐷 , we show that asequence of a Toeplitz operator π‘‡πœ‘π‘–π‘— are analytic if πœ‘π‘–π‘— 𝑖𝑠 𝑖𝑛 𝐻 . Theseare easily seen to be subnormal:Where πΏπœ‘π‘–π‘— are normal operator of multiplication by πœ‘π‘–π‘— in 𝐿 (πœ•π·) .Lastly, for πœ‘π‘–π‘— ∈ 𝐿 we show that, the sequence of Toeplitz operatorπ‘‡πœ‘π‘–π‘— on the Bergman space with symbol πœ‘π‘–π‘— given by:are analytic if πœ‘π‘–π‘— ∈ 𝐻 .

Zenodo (CERN European Organization for Nuclear Research)
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Holomorphic and Operator Theory
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