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Bounded Linear Operators on Hilbert Spaces

In: Basic Classes of Linear Operators

Author

Listed:
  • Israel Gohberg

    (Tel Aviv University, School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences)

  • Seymour Goldberg

    (University of Maryland, Department of Mathematics)

  • Marinus A. Kaashoek

    (Vrije Universiteit Amsterdam, Department of Mathematics and Computer Science)

Abstract

In this chapter, continuous linear functions defined on a Hilbert space are introduced and studied. These functions are described by infinite matrices in the same way as linear transformations on ℂ n 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.

Suggested Citation

  • Israel Gohberg & Seymour Goldberg & Marinus A. Kaashoek, 2003. "Bounded Linear Operators on Hilbert Spaces," Springer Books, in: Basic Classes of Linear Operators, chapter 0, pages 51-133, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7980-4_2
    DOI: 10.1007/978-3-0348-7980-4_2
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