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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 8736
   School of Mathematics
  Title: Compact linear operators between probabilistic nomed spaces
  Author(s): K. Nourouzi
  Status: Published
  Journal: Oper. Theory Adv. Appl.
  Vol.: 181
  Year: 2008
  Pages: 347-353
  Supported by: IPM
  Abstract:
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 Nx, and Nx(t) is the value Nx, at t ∈ \mathbbR satisfying the following conditions:

    (NI) Nx(0) = 0,
    (N2) Nx(t) = 1 for all t > 0 iff x = 0,
    (N3) Nax(t) = Nx([(t)/(|α|)]) for all α ∈ \mathbbR\{0},
    (N4) Nx+y(s + t) ≥ min{Nx(s), Ny(t)} for all x, yX, and s,t ∈ \mathbbR0+
In this article, we study compact linear operators between probabilistic normed spaces.

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