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Elliptic operators and their symbols

Vasilyev Vladimir

Demonstratio Mathematica

2019

Vol. 52, nr 1

361--369

We consider special elliptic operators in functional spaces on manifolds with a boundary which has some singular points. Such an operator can be represented by a sum of operators, and for a Fredholm property of an initial operator one needs a Fredholm property for each operator from this sum.

Weak sequential completeness and compactness in topological function spaces

Nowak M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr spec.

155-165

Let (E, r) be a Hausdorff locally convex-solid function space (over a cr-finite measure space) and let E* stand for its topological dual. It is proved that the space (E, r) is weakly sequentially complete if and only if r is a c-Lebesgue and cr-Levy topology. In particular, a characterization of weak sequential completeness of Or-licz spaces L* in terms of Orlicz functions is given. Moreover, it is proved that the Eberlein-Smulian type theorem remains valid for a locally convex space (E, o~(E, E*)). A characterization of conditional and relative weak compactness in (E, r) is obtained.

C[sub p](X) is not G[sub delta, sigma] : a simple proof

Mill J.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 4

319-323

It is known that if C[sub p](X) is a G[sub delta, sigma]-subset of R[sup x] then X is discrete. We present a simple proof of this.

Game-theoretic approach to the hereditary Baire property of Cp(Nf)

Michalewski H.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 2

135-140

We characterize second category P-filters on omega in terms of topological games. These characterizations use strong Choquet game gamma in the function space C[sub p](N[sub F]) associated with the filter F and a certain game delta played on the filter F. This complements earlier characterizations of hereditary Baire spaces C[sub p](N[sub F]), given by Gul'ko, Sokolov and Marciszewski.

On approximation by linear integral operations in function spaces

Musielak A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1998

[Z] 38

93-99

The are given theorems on approximation of random functions by means of linear operators in function spaces.