Semi-Fredholm Toeplitz operators on the space of real analytic functions

Jasiczak, M.

doi:10.4064/sm170810-23-5

Cited by 6 publications

(16 citation statements)

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“…The statements concerning the codimension of the range of T F in Corollary 2.3 and the dimension of the kernel of T F in Corollary 2.4 are immediate consequences of the Coburn-Simonenko theorem for Toeplitz operators on A(R), which we proved in ( [28], Theorem 1.2). This says, as in the Hardy space case, that either ker T F or ker T F is trivial.…”

Section: Corollary 24 Consider a Toeplitz Operator T F : A(r) → A(rmentioning

confidence: 77%

“…The proofs of both Theorems 1 and 2 are based on the characterization of semi-Fredholm operators obtained in [28]. In order to present the idea of the proof we recall now these results.…”

Section: Resultsmentioning

confidence: 99%

“…Our work relies heavily on the previous results concerning Fredholm Toeplitz operators [9,27] and semi-Fredholm operators [28]. We also use extensively the Köthe-Grothendieck-da Silva duality.…”

Section: Corollary 24 Consider a Toeplitz Operator T F : A(r) → A(rmentioning

confidence: 99%

“…For more details we refer to our previous works [9,27] and, especially, [28]. We refer the reader to [26,36] and [30] for the functional analytic background.…”

Section: The Space Of Real Analytic Functionsmentioning

confidence: 99%

“…We recall now the definition of the Cauchy transform on the space X (R) following the presentation in [28]. Let F ∈ X (R) and let F be the equivalence class of a functionF ∈ H(U \K), i.e.…”

Section: Symbol Space and Toeplitz Operatorsmentioning

confidence: 99%

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One-Sided Invertibility of Toeplitz Operators on the Space of Real Analytic Functions on the Real Line

Jasiczak

Golińska

2020

Integr. Equ. Oper. Theory

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We show that a Toeplitz operator on the space of real analytic functions on the real line is left invertible if and only if it is an injective Fredholm operator, it is right invertible if and only if it is a surjective Fredholm operator. The characterizations are given in terms of the winding number of the symbol of the operator. Our results imply that the range of a Toeplitz operator (and also its adjoint) is complemented if and only if it is of finite codimension. Similarly, the kernel of a Toeplitz operator (and also its adjoint) is complemented if and only if it is of finite dimension.

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Section: Corollary 24 Consider a Toeplitz Operator T F : A(r) → A(rmentioning

confidence: 77%

“…The proofs of both Theorems 1 and 2 are based on the characterization of semi-Fredholm operators obtained in [28]. In order to present the idea of the proof we recall now these results.…”

Section: Resultsmentioning

confidence: 99%

Section: Corollary 24 Consider a Toeplitz Operator T F : A(r) → A(rmentioning

confidence: 99%

“…For more details we refer to our previous works [9,27] and, especially, [28]. We refer the reader to [26,36] and [30] for the functional analytic background.…”

Section: The Space Of Real Analytic Functionsmentioning

confidence: 99%

Section: Symbol Space and Toeplitz Operatorsmentioning

confidence: 99%

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