Wyniki wyszukiwania - BazTech

1

Multiplication operators on weighted Banach spaces of analytic functions with exponential weights

Bogalska K.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2001

|

Vol. 49, no 4

409-416

EN

Let v be the weight on the disc and M[phi] be the pointwise multiplication operator, M[phi](f) = [phi]f, on the weighted Banach space of analytic functions H[...](D) on the disc with the sup-norms. We characterize when M[phi] : H[...] --> H[...] is an isomorphism into for weights tending exponentially to zero at the boundary. In particular, the result holds for v(z) = exp[...] or v(z) = exp [...] for any [delta] > 0.

2

The dimension of self-similar measures

Szarek T.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2000

|

Vol. 48, no 3

293-302

EN

We consider Iterated Function Systems on Polish spaces. The Hausdorff dimension of invariant distributions for such systems is estimated.

3

Non-linearity of the set of p-quasi-analytic vectors for some essentially self-adjoint operators

Rusinek J.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2000

|

Vol. 48, no 3

287-292

EN

We show that, for any p [is greater than or equal to] 1, there exists an essentially self-adjoint operator for which the set of p-quasi-analytic vectors is not linear.

4

Complex interpolation of spaces of operators on l1

Defant A., Michels C.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2000

|

Vol. 48, no 3

303-318

EN

Within the theory of complex interpolation and 0-Hilbert spaces we extend classical results of Kwapień on absolutely (r,1)-summing operators on l1 with values in lp as well as their natural extensions for mixing operators invented by Maurey. Furthermore, we show that for 1 < p < 2 every operator on l1 with values in a 0-type 2 space, 0 = 2/p', is Rademacher p-summing. This is another extension of Kwapień's results, and by an extrapolation procedure a natural supplement to a statement of Pisier.

5

Convergence of Picard iterates of nonexpansive mappings

Kirk W., Sims B.

Bulletin of the Polish Academy of Sciences. Mathematics

|

1999

|

Vol. 47, no 2

147-155

EN

Let X be a Banach space, C a closed subset of X, and T : C --> C a nonexpansive mapping. Conditions are given which assure that if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). If T is asymptotically regular, it suffices to assume that the closed subsets of X are densely proximinal and that nested spheres in X have compact interfaces. Such spaces include, among others, those which have Rolewicz's property ([beta]). If X has strictly convex norm the asymptotic regularity assumption can be dropped and the nested sphere property holds trivially. Consequently the result holds for all reflexive locally uniformly convex spaces.

6

Square functions for wavelet type systems

Gevorkjan G., Wolnik B.

Bulletin of the Polish Academy of Sciences. Mathematics

|

1998

|

Vol. 46, no 2

155-171

EN

We show the equivalence of the L[sub p] (0 < p [a is less than or equal to] 2) (quasi)-norms of square functions for the systems {2 [...], where f satisfies some decay condition. This implies the boundedness of the shift operator on the wavelet type unconditional basis on L[sub p], 1 < p < [infinity]. We prove also that such operator is unbounded on L[sub 1].

7

On summing and related operators acting from a Hilbert space

Tien N., Tarieladze V., Vidal R.

Bulletin of the Polish Academy of Sciences. Mathematics

|

1998

|

Vol. 46, no 4

365-375

EN

We study the situation when the behaviour of an operator from a Hilbert space to a Banach space on all orthonormal bases determines whether it belongs to a prescribed class of operators. The cases of (q, 2)-summing, almost summing and [gamma]-summing operators are treated in a unified way.

8

On normal extensions of unobounded operators

Ota S.

Bulletin of the Polish Academy of Sciences. Mathematics

|

1998

|

Vol. 46, no 3

291-301

EN

Subnormality of unbounded operators in a Hilbert space is studied. It is shown that a closed subnormal operator, unlike a closed symmetric operator, has not necesarily a normal extension of the second kind (in terms of Naimark). In connection with this, the uniqueness of the normal extension to the same Hilbert space is discussed.

9

Generalized vector quasi-variational inequalities

Song W.

Bulletin of the Polish Academy of Sciences. Mathematics

|

1998

|

Vol. 46, no 4

401-417

EN

First we establish a general existence theorem for a generalized vector qusi-variational inequality in a topological vector space by using a set-valued and vector generalization of Ky Fan minimax principle. As applications, several existence theorems for generalized vector quasi-variational inequalities are derived under assumptions of order-lower (order-upper) semicontinuity or monotonicity of set-valued mappings.

10

A nonstandard difference Sturm-Liouville operator

Javorskij J., Ljance V.

Bulletin of the Polish Academy of Sciences. Mathematics

|

1998

|

Vol. 46, no 3

285-290

EN

After Nelson's Radically Elementary Probability Theory [1] a natural question arises: whether a hyperfinite-dimensional space is sufficiently rich to be used for the same goal as an infinite-dimensional one. Here a hyperfinite 3-diagonal matrix is investigated, which spectral properties are simular to the Naimarks's singular nonselfadjoint Sturm-Liouville differential operator on semi-axis [2, 3].