Titlebook: Basic Operator Theory; Israel Gohberg,Seymour Goldberg Textbook 2001 Birkhäuser Boston 2001 Applications of Mathematics.Functional Analysi

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Linear Operators on a Banach Space,Many of the definitions, theorems and proofs concerning operators in .(., .) carry over verbatim to operators in .(., .), where X and Y are Banach spaces.

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Bounded Linear Operators on Hilbert Spaces,in the same way as linear transformations on ℂ. are represented by finite matrices. In this way the chapter may be viewed as a beginning of a theory of infinite matrices. As may be expected, analysis plays a very important role.

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Non Linear Operators,tors, again the main problem is to solve equations Ax = y for a nonlinear A in a Hilbert or Banach space. Geometrically, this problem means that a certain map or operator B leaves fixed at least one vector x, i.e., x = Bx, where Bx = x + Ax − y, and we have to find this vector. Theorems which establ

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