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Aspects of deltaconvexity /Duda, Jakub, January 2003 (has links)
Thesis (Ph. D.)University of MissouriColumbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 8389). Also available on the Internet.

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Aspects of deltaconvexityDuda, Jakub, January 2003 (has links)
Thesis (Ph. D.)University of MissouriColumbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 8389). Also available on the Internet.

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Complemented and uncomplemented subspaces of Banach spacesVuong, Thi Minh Thu January 2006 (has links)
"A natural process in examining properties of Banach spaces is to see if a Banach space can be decomposed into simpler Banach spaces; in other words, to see if a Banach space has complemented subspaces. This thesis concentrates on three main aspects of this problem: norm of projections of a Banach space onto its finite dimensional subspaces; a class of Banach spaces, each of which has a large number of infinite dimensional complemented subspaces; and methods of finding Banach spaces which have uncomplemented subspaces, where the subspaces and the quotient spaces are chosen as wellknown classical sequence spaces (finding nontrivial twisted sums)." Abstract. / Master of Mathematical Sciences

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Complemented and uncomplemented subspaces of Banach spacesVuong, Thi Minh Thu . University of Ballarat. January 2006 (has links)
"A natural process in examining properties of Banach spaces is to see if a Banach space can be decomposed into simpler Banach spaces; in other words, to see if a Banach space has complemented subspaces. This thesis concentrates on three main aspects of this problem: norm of projections of a Banach space onto its finite dimensional subspaces; a class of Banach spaces, each of which has a large number of infinite dimensional complemented subspaces; and methods of finding Banach spaces which have uncomplemented subspaces, where the subspaces and the quotient spaces are chosen as wellknown classical sequence spaces (finding nontrivial twisted sums)." Abstract. / Master of Mathematical Sciences

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Linear OperatorsMalhotra, Vijay Kumar 12 1900 (has links)
This paper is a study of linear operators defined on normed linear spaces. A basic knowledge of set theory and vector spaces is assumed, and all spaces considered have real vector spaces. The first chapter is a general introduction that contains assumed definitions and theorems. Included in this chapter is material concerning linear functionals, continuity, and boundedness. The second chapter contains the proofs of three fundamental theorems of linear analysis: the Open Mapping Theorem, the HahnBanach Theorem, and the Uniform Boundedness Principle. The third chapter is concerned with applying some of the results established in earlier chapters. In particular, the concepts of compact operators and Schauder bases are introduced, and a proof that an operator is compact if and only if its adjoint is compact is included. This chapter concludes with a proof of an important application of the Open Mapping Theorem, namely, the Closed Graph Theorem.

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