Compact Linear Operators Between Probabilistic Normed Spaces

  • Kourosh Nourouzi
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 181)


A pair (X, N) is said to be a probabilistic normed space if X is a real vector space, N is a mapping from X into the set of all distribution functions (for xX, the distribution function N(x) is denoted by N x , and N x (t) is the value N x at t ∈ ℝ) satisfying the following conditions:
  1. (N1)

    N x (0) = 0

  2. (N2)

    N x (t) = 1 for all t > 0 iff x = 0

  3. (N3)

    N αx (t) = N x \( (\frac{t} {{|\alpha |}})\) for all α ∈ ℝ∖0,

  4. (N4)

    N x+y (s + t) ≥ min N x (s), N y (t) for all x, yX, and s, t ∈ ℝ0 +.


In this article, we study compact linear operators between probabilistic normed spaces.


Compact operator PN-space bounded set N-compact set weakly bounded operator strongly bounded operator 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Kourosh Nourouzi
    • 1
    • 2
  1. 1.Department of MathematicsK. N. Toosi University of TechnologyTehranIran
  2. 2.Institute for Studies in Theoretical Physics and Mathematics (IPM)TehranIran

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