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Petković, Katarina I. 1975-

Karakterizacija ograničenih linearnih i kompaktnih operatora izmedju BK prostora

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Academic metadata

Doktorska disertacija

Prirodno-matematičke nauke

Univerzitet u Nišu

Prirodno-matematički fakultet

Odsek za matematiku i informatiku

Other Theses Metadata

Characterization of bounded linear and compact operators between BK spaces

[K. I. Petković]

94 str.

Biografija autora: str. [99-100]

Datum odbrane:21.07.2016.

mathematical analysis

Đolović, Ivana (mentor)

Rakočević, Vladimir 1953- (član komisije)

Đorđević, Dragan 1970- (član komisije)

Malkowsky, Eberhard (član komisije)

Within this thesis , the new sequence spaces are introduced
and the similarities and the differences between the matrix
transformations and the general linear bounded operators on BK
spaces are considered. The characterization of matrix
transformations between new-defined sequence spaces is done by
applying the theory of FK and BK spaces along with the results
related to matrix domains of triangles. In some cases, where it is
possible, the representation of general linear bounded operator is
given by infinite matrix.
Further on, the condition for compactness of certain classes
of operators are given. Applying the Hausdorff measure of
noncompactness, the necessary and sufficient conditions for
compactness are obtained. In the cases where it is not possible, and
where instead of the exact value we can only get the estimations for
the measure of noncompactness of the operator, the results of
Sargent are applied. This thesis contains some of such, improved,
examples but also the new results concerning the newly defined
spaces. The cases in which one can not apply the Hausdorff
measure, nor the results of Sargent, are examined too, and the
special properties of considered sequence spaces are used to obtain
the characterizations of compact operators. In certain situations the
results of compactness are formulated for the general bounded
linear operators as well as for the matrix linear operators.

functional analysis

funkcionalna analiza

517.982.2+517.983(043.3)

Serbian

1025344745

Elektronska teza

Within this thesis , the new sequence spaces are introduced
and the similarities and the differences between the matrix
transformations and the general linear bounded operators on BK
spaces are considered. The characterization of matrix
transformations between new-defined sequence spaces is done by
applying the theory of FK and BK spaces along with the results
related to matrix domains of triangles. In some cases, where it is
possible, the representation of general linear bounded operator is
given by infinite matrix.
Further on, the condition for compactness of certain classes
of operators are given. Applying the Hausdorff measure of
noncompactness, the necessary and sufficient conditions for
compactness are obtained. In the cases where it is not possible, and
where instead of the exact value we can only get the estimations for
the measure of noncompactness of the operator, the results of
Sargent are applied. This thesis contains some of such, improved,
examples but also the new results concerning the newly defined
spaces. The cases in which one can not apply the Hausdorff
measure, nor the results of Sargent, are examined too, and the
special properties of considered sequence spaces are used to obtain
the characterizations of compact operators. In certain situations the
results of compactness are formulated for the general bounded
linear operators as well as for the matrix linear operators.