Linear Transformations

  • Jürg T. Marti
Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 18)


In the four paragraphs of this chapter we present some basic definitions and facts from functional analysis, as well as applications in special spaces. These preliminaries will be used in the subsequent chapters. Since many introductions to functional analysis are now available, in order to save space, we omit proofs of all of the lemmas, theorems and corollaries given here. Moreover, one will find here only the working tools which are really needed for the development of the theory of bases. We begin by defining various abstract spaces, and we list their most important properties. Then we investigate linear transformations of one space into another, continue with some facts on conjugate spaces, and conclude with results for several spacial spaces.


Banach Space Linear Space Linear Transformation Linear Subspace Weak Topology 
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  1. Bourbaki,N. Espaces vectoriels topologiques, Ch. I-V, Elements de mathématique V. Paris, 1953–55.MATHGoogle Scholar
  2. Day, M. M. Normed linear spaces. Berlin-Göttingen-Heidelberg, 1962.MATHGoogle Scholar
  3. Dieudonné, J. Foundations of modern analysis. New York, 1960.MATHGoogle Scholar
  4. Dunford, N., and J. T. Schwartz Linear operators, New York, I (1958), II (1963).MATHGoogle Scholar
  5. Edwards, R. E. (see also Arsove, M. G.) Functional analysis, theory and applications. New York, 1965.MATHGoogle Scholar
  6. Halmos, P. R. Finite dimensional vector spaces. Princeton, 1958.MATHGoogle Scholar
  7. Halmos, P. R. A Hilbert space problem book. Princeton, 1967.MATHGoogle Scholar
  8. Hausdorff, F. Mengenlehre. New York, 1944.MATHGoogle Scholar
  9. Hille, E., and R. S. Phillips Functional analysis and semi-groups. Amer. Math. Soc. Colloquium Publ. 31 (rev. ed.) (1957).Google Scholar
  10. Kelley, J. L., and I. Namioka Linear topological spaces. Princeton, 1963.MATHGoogle Scholar
  11. Köthe, G. Topologische lineare Räume. Berlin-Heidelberg-New York, 1966.MATHGoogle Scholar
  12. Rickart, C. E. General theory of Banach algebras. Princeton, 1960.MATHGoogle Scholar
  13. Taylor, A. E. Introduction to functional analysis. New York, 1958.MATHGoogle Scholar
  14. Wilansky, A. Functional analysis. New York, 1964.MATHGoogle Scholar
  15. Yosida, K. Functional analysis. Berlin-Göttingen-Heidelberg, 1965.MATHGoogle Scholar
  16. Zygmund, A. (see also Paley, R. E. A. C.) Trigonometrical series. Warsaw, 1935.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1969

Authors and Affiliations

  • Jürg T. Marti
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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