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2 results

  • 6 - Linear Operators

  • from Part II - Elements Of Classical Functional Analysis
  • Martin Buntinas, Loyola University, Chicago
  • Book:
    Classical and Discrete Functional Analysis with Measure Theory
    Published online:
    06 January 2022
    Print publication:
    20 January 2022, pp 214-252

  • Summary

    Linear Operators and Linear Functionals are studied. Then Operator Spaces, Topological Duals, and Second Duals of Normed Spaces are considered. Lebesgue L(p) Spaces are defined and studied. The theorems of Hahn–Banach Extension, Baire Category, Riesz Representation, Open Mapping, Closed Graph, and Banach Fixed Points are all proven.

  • Multifunctions and Inverse Cluster Sets

  • James E. Joseph
  • Journal:
    Canadian Mathematical Bulletin / Volume 23 / Issue 2 / 01 June 1980
    Published online by Cambridge University Press:
    20 November 2018, pp. 161-171
    Print publication:
    01 June 1980
    • Article
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  • In this paper the notion of inverse cluster set, which was recently introduced and studied for functions by T. R. Hamlett and P. E. Long (Proc. Amer. Math. Soc, 53 (1975), 470-476), is extended to and investigated for multifunctions. We generalize the notion of inverse cluster set, extend to multifunctions and generalize some known results for inverse cluster sets of functions and offer some new results. In the latter sections, compactness generalizations are characterized in terms of inverse cluster sets and some results on connected and conectivity functions are extended to multifunctions.