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Best approximation in quotient probabilistic normed space

Sen M., Nath S., Tripathy B. C.

Journal of Applied Analysis

2017

Vol. 23, nr 1

53--57

In this article, we study the best approximation in quotient probabilistic normed space. We define the notion of quotient space of a probabilistic normed space, then prove some theorems of approximation in quotient space are extended to quotient probabilistic normed space.

On the moment measure conjecture

Białynicki-Birula A.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 1

33-40

The main purpose of the paper is to give a characterization of such open invariant subsets U of projective spaces with an action of a torus T, which admit a good quotient U --> U//T and the quotient space is compact. It follows from the result that moment measure conjecture (stated in [4]) is valid in the case of projective spaces (and their products).

The separable quotient problem for symmetric function spaces

Śliwa W.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 1

13-27

We study the separable quotient problem for some classes of symmetric function spaces on a measure space (Omega,Sigma,mi). In particular we prove that an infinite dimensional Orlicz space L[sup fi](Omega,Sigma,mi) has an infinite dimensional separable quotient if and only if the dual of L[sup fi](Omega,Sigma,mi) is total or there exists a measurable subset A of[Omega] such that the space L[sup fi] (Alpha,Sigma[sub Alpha],mi[sub Alpha)) is infinite dimensional and separable.