Some Basic Properties of Polynomials in a Linear Relation in Linear Spaces

Sandovici, Adrian

doi:10.1007/978-3-7643-8270-4_14

Cited by 18 publications

(4 citation statements)

References 5 publications

(6 reference statements)

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“…Therefore, Q TS TQ −1 S and Q S S are bounded operators in Banach spaces such that Q TS TS = (Q TS TQ −1 S )(Q S S) and by Lemma 3.3 (iii) we have Q TS TS ∈ Φ + , hence TS ∈ Φ + . In this situation by [21] we have that Q S S is a Φ + -operator and thus S ∈ Φ + by virtue of Lemma 3.3 (iii). Now, we extend Theorem 1.1 (ii) to linear relations.…”

Section: Fredholm and Semi-fredholm Perturbationmentioning

confidence: 93%

On a characterization of the essential spectra

Abdmouleh

Álvarez

Jeribi

2022

Filomat

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Section: Fredholm and Semi-fredholm Perturbationmentioning

confidence: 93%

On a characterization of the essential spectra

Abdmouleh

Álvarez

Jeribi

2022

Filomat

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“…We claim that for each λ ∈ C \ R the linear relation p(S + ) (see, e.g., [9,26]), can be decomposed in the form…”

Section: Theorem 22 Let a And B Be Selfadjoint Operators In The Krementioning

confidence: 99%

On finite rank perturbations of definitizable operators

Azizov

Behrndt

Trunk

2008

Journal of Mathematical Analysis and Applications

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It was shown by P. Jonas and H. Langer that a selfadjoint definitizable operator A in a Krein space remains definitizable after a finite rank perturbation in resolvent sense if the perturbed operator B is selfadjoint and the resolvent set ρ(B) is nonempty. It is the aim of this note to prove a more general variant of this perturbation result where the assumption on ρ(B) is dropped. As an application a class of singular ordinary differential operators with indefinite weight functions is studied.

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“…The behaviour of the domain, the range, the null space and the multivalued part of p(T ) is described in the following lemma which is due to Sandovici [21].…”

Section: Definition 14 ([21 1])mentioning

confidence: 99%

On regular linear relations

Álvarez

2011

Acta. Math. Sin.-English Ser.

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For a closed linear relation in a Banach space the concept of regularity is introduced and studied. It is shown that many of the results of Mbekhta and other authors for operators remain valid in the context of multivalued linear operators. We also extend the punctured neighbourhood theorem for operators to linear relations and as an application we obtain a characterization of semiFredholm linear relations which are regular.

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Some Basic Properties of Polynomials in a Linear Relation in Linear Spaces

Abstract: Abstract. The behavior of the domain, the range, the kernel and the multivalued part of a polynomial in a linear relation is analyzed, respectively. Mathematics Subject Classification (2000). Primary 47A05; Secondary 47A06.

Cited by 18 publications

References 5 publications

On a characterization of the essential spectra

On a characterization of the essential spectra

On finite rank perturbations of definitizable operators

On regular linear relations

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