Postgraduate Thesis uoadl:2936546 389 Read counter

Κατεύθυνση Θεωρητικά Μαθηματικά

Library of the School of Science

Library of the School of Science

2021-02-22

2021

Zamanis Orestis

Γεράσιμος Μπαρμπάτης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ

Ιδεώδη Χώρων Τελεστών και Θεωρία Calkin

Greek

Operator Ideals and Calkin Theory

In this thesis we will study compact operators in combination with ideals of the space of bounded operators in which are defined norms.

In the first section we study the compact operators at separable Hilbert spaces, emphasizing at fundamental properties of the values and singular values of them just as and the connection which there is between of them. In the second section we study ideals of operators, begining from symmetrical norms at suitable space of consequences which are expended normally at concrete category ideals. Then we will define the Calkin's space as a space of consequences

and we 'll correspond the ideals with the Calkin's spaces with a particular way. The section ends with a report of concrete results in relation to ideals of the category $J_p$, $1\leq p < \infty$. In the third section we study the trace of operators which belongs to $J_1$, something which is indispensable for the development of a result in relation to Schatten's dual theory. Then we 'll combine the trace with the values of operator which belongs to $J_1$ for the formality and proof of Lidskii's theorem. In the forth section we use the ideals of the category $J_p$, $1\leq p < \infty$, for studying operators $g(i\triangledown)$. For the achieving of comprehension these operators we need some conceptions from the Sobolev spaces and the indispensable foundation from the Fourier theory.

In the first section we study the compact operators at separable Hilbert spaces, emphasizing at fundamental properties of the values and singular values of them just as and the connection which there is between of them. In the second section we study ideals of operators, begining from symmetrical norms at suitable space of consequences which are expended normally at concrete category ideals. Then we will define the Calkin's space as a space of consequences

and we 'll correspond the ideals with the Calkin's spaces with a particular way. The section ends with a report of concrete results in relation to ideals of the category $J_p$, $1\leq p < \infty$. In the third section we study the trace of operators which belongs to $J_1$, something which is indispensable for the development of a result in relation to Schatten's dual theory. Then we 'll combine the trace with the values of operator which belongs to $J_1$ for the formality and proof of Lidskii's theorem. In the forth section we use the ideals of the category $J_p$, $1\leq p < \infty$, for studying operators $g(i\triangledown)$. For the achieving of comprehension these operators we need some conceptions from the Sobolev spaces and the indispensable foundation from the Fourier theory.

Science

Operators, Ideals, Consequences

No

0

No

4

137

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diplomatiki.pdf

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