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Showing 1 to 18 of 18 for “"Compact operators."”.
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Spaces of Compact Operators
… dissertation we study the structure of spaces of operators, especially the space of all compact operators between two Banach spaces X and Y. Work by Kalton, Emmanuele, Bator and Lewis on the space of compact and weakly compact operators motivates much of this paper. Let L(X,Y) be the Banach space …
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On the Numerical Range of Compact Operators
<p>One of the many characterizations of compact operators is as linear operators which<br />can be closely approximated by bounded finite rank operators (theorem 25). It is<br />well known that the numerical range of a bounded operator on a finite dimensional<br />Hilbert space is closed (theorem …
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Ideals in von Neumann algebras and in associated operator algebras
The compact operators on a Hilbert space are those operators for which the image of the unit ball is relatively compact in the norm topology. These operators form an ideal, in the algebra of all continuous linear operators on the Hilbert space, which is closed in the uniform norm. In the case that …
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Complemented Subspaces of Bounded Linear Operators
… complemented in the space of all bounded linear operators. In this dissertation the complementation of various classes of operators in the space of all bounded linear operators is considered. This paper begins with a preliminary discussion of linear bounded operators as well as operator ideals. …
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Ascent, descent, nullity and defect of linear operators
… to be a survey of nullity and defect of linear operators on the one hand, and ascent and descent on the other, and the relationships between these concepts. These quantities are of considerable use in the discussion of linear operators, e.g. compact operators.
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Minimax in the theory of operators on Hilbert spaces and Clarkson-McCarthy estimates for lq (Sp) spaces of operators in the Schatten ideals
… in this thesis are the minimax theorems for operators in Schatten ideals of compact operators acting on separable Hilbert spaces, generalized Clarkson-McCarthy inequalities for vector lq-spaces lq (Sp) of operators from Schatten ideals Sp, inequalities for partitioned operators and for …
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Ideals and Commutators of Operators
<p>Subideals. A subideal of operators is an ideal of J (called a J-ideal) for J an arbitraryideal of B(H). Necessary and sufficient conditions are determined for a finitely generatedsubideal to be also an ideal of B(H) and then these conditions are exploited to characterizeall finitely generated …
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Nonstandard theory of vector measures
… representing measures of both absolutely summing operators and weakly compact operators, as well as solutions of problems concerning the range of a vector measure.
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Algebras of Toeplitz Operators
In this work we examine C*-algebras of Toeplitz operators over the unit ball in ℂ<sup>n</sup> and the unit polydisc in ℂ². Toeplitz operators are interesting examples of non-normal operators that generate non-commutative C*-algebras. Moreover, in the nice cases (depending on the geometry of the …
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Dunford-Pettis Sets and Operators
Sets in Banach spaces that are mapped into norm compact sets by weakly compact operators (called Dunford-Pettis sets) are studied in general and in the spaces L(,1) ((mu),X), C((OMEGA),X), and P(,1)((mu),X). It is shown that if X is a Banach space with the Dunford-Pettis property and X contains no …
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Unbound linear operators in operator ranges
… part be considering unbounded or closed linear operators instead of continuous everywhere defined linear operators. We will not be attempting to give exhaustive coverage of unbounded linear operators but will try to give some insight into the use of operator range techniques in the theory of …
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Sequences of compact curvature
… differential of a (cochain-)complex by "small" operators, one obtains what is referred to as quasicomplexes, i.e. a sequence whose curvature is not equal to zero in general. In this situation the cohomology is no longer defined. Note that it depends on the structure of the underlying spaces …
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Unbounded linear operators in seminormed spaces
… (for example, seminorms occur in the study of operators of the Tauberian type (see [C2]) and operators analagous to weakly compact operators (see Chapter VI). It is the aim of this work to generalise as much of the basic theory of unbounded linear operators as possible to seminormed spaces. In …
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On Symmetric Operator Ideals and s-Numbers
… <em>T</em>∗ between Banach spaces. For non-compact operator <em>T</em> ∈ <em>L</em>(<em>X, Y</em> ), we do not have a lot of information about the relationship between n-th <em>s</em>-number, <em>s</em><em>n</em>(T), with <em>s</em><em>n</em>(<em>T</em>∗ ), however, in chapter 2, by …
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ΜΕΛΕΤΗ ΤΩΝ ΡΙΖΩΝ ΜΙΚΤΩΝ ΣΥΝΑΡΤΗΣΕΩΝ BESSEL
WE STUDY THE EXISTENCE OR NOT OF THE COMPLEX AND REAL ZEROS OF MIXED BESSEL FUNCTIONS, MV(Z)=F(Z)JV(Z)+G(Z)JV'(Z), OF FIRST KIND AND ORDER V (IN GENERAL COMPLEX). THE MULTIPLICITY OF THE ZEROS OF THE DERIVATIVES OF BESSEL FUNCTIONS JV(S)(Z), S=1,2,3,4 IS ALSO EXAMINED. FOR THE FUNCTION JV''(Z), …