Wyniki wyszukiwania

1

On vector-valued inequalities for Sidon sets and sets of interpolation

100%

Kalton N. J.

Colloquium Mathematicum

|

1993

|

tom 64

|

nr 2

233-244

EN

Let E be a Sidon subset of the integers and suppose X is a Banach space. Then Pisier has shown that E-spectral polynomials with values in X behave like Rademacher sums with respect to $L_p$-norms. We consider the situation when X is a quasi-Banach space. For general quasi-Banach spaces we show that a similar result holds if and only if E is a set of interpolation ($I_0$-set). However, for certain special classes of quasi-Banach spaces we are able to prove such a result for larger sets. Thus if X is restricted to be "natural" then the result holds for all Sidon sets. We also consider spaces with plurisubharmonic norms and introduce the class of analytic Sidon sets.

2

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A note on galbed spaces

100%

Kalton N. J.

Commentationes Mathematicae

|

1980

|

tom 21

|

nr 1

EN

The article contains no abstract

3

Calderón couples of rearrangement invariant spaces

100%

Kalton N. J.

Studia Mathematica

|

1993

|

tom 106

|

nr 3

233-277

EN

We examine conditions under which a pair of rearrangement invariant function spaces on [0,1] or [0,∞) form a Calderón couple. A very general criterion is developed to determine whether such a pair is a Calderón couple, with numerous applications. We give, for example, a complete classification of those spaces X which form a Calderón couple with $L_∞.$ We specialize our results to Orlicz spaces and are able to give necessary and sufficient conditions on an Orlicz function F so that the pair $(L_F,L_∞)$ forms a Calderón pair.

4

Uniqueness of unconditional bases in $c_0$-products

64%

Casazza P., Kalton N. J.

Studia Mathematica

|

1999

|

tom 133

|

nr 3

275-294

EN

We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does $c_0(X)$. We also give some positive results including a simpler proof that $c_0(ℓ_1)$ has a unique unconditional basis and a proof that $c_0(ℓ_{p_n}^{N_n})$ has a unique unconditional basis when $p_n ￬ 1$, $N_{n+1} ≥ 2N_{n}$ and $(p_n-p_{n+1}) logN_{n}$ remains bounded.

5

A remark on a problem of Klee

64%

Kalton N. J., Peck N. T.

Colloquium Mathematicum

|

1996

|

tom 71

|

nr 1

1-5

6

Unconditional ideals in Banach spaces

52%

Godefroy G., Kalton N. J., Saphar P. D.

Studia Mathematica

|

1993

|

tom 104

|

nr 1

13-59

EN

We show that a Banach space with separable dual can be renormed to satisfy hereditarily an "almost" optimal uniform smoothness condition. The optimal condition occurs when the canonical decomposition $X*** = X^{⊥} ⊕ X*$ is unconditional. Motivated by this result, we define a subspace X of a Banach space Y to be an h-ideal (resp. a u-ideal) if there is an hermitian projection P (resp. a projection P with ∥I-2P∥ = 1) on Y* with kernel $X^{⊥}$. We undertake a general study of h-ideals and u-ideals. For example we show that if a separable Banach space X is an h-ideal in X** then X has the complex form of Pełczyński's property (u) with constant one and the Baire-one functions Ba(X) in X** are complemented by an hermitian projection; the converse holds under a compatibility condition which is shown to be necessary. We relate these ideas to the more familiar notion of an M-ideal, and to Banach lattices. We further investigate when, for a separable Banach space X, the ideal of compact operators K(X) is a u-ideal or an h-ideal in ℒ(X) or K(X)**. For example, we show that K(X) is an h-ideal in K(X)** if and only if X has the "unconditional compact approximation property" and X is an M-ideal in X**.

7

Analytic functions in non-locally convex spaces and applications

38%

Kalton N. J.

Studia Mathematica

|

1986

|

tom 83

|

nr 3

275-303

8

Bases and basic sequences in F-spaces

32%

Kalton N. J., Shapiro J. H.

Studia Mathematica

|

1976

|

tom 56

|

nr 1

47-61

9

Plurisubharmonic functions on quasi-Banach spaces

32%

Kalton N. J.

Studia Mathematica

|

1986

|

tom 84

|

nr 3

297-324

10

On operators on $L_0$

32%

Kalton N. J.

Colloquium Mathematicum

|

1984

|

tom 48

|

nr 1

81-88

11

Schauder bases and reflexivity

26%

Kalton N. J.

Studia Mathematica

|

1970

|

tom 38

|

nr 1

255-266

12

Unconditional and normalised bases

26%

Kalton N. J.

Studia Mathematica

|

1970

|

tom 38

|

nr 1

248-253

13

Universal spaces and universal bases in metric spaces

26%

Kalton N. J.

Studia Mathematica

|

1977

|

tom 61

|

nr 2

161-191

14

Quotients of $L_{p}(0,1)$ for 0 ≤ p < 1

23%

Kalton N. J., Peck N. T.

Studia Mathematica

|

1979

|

tom 64

|

nr 1

65-75

15

Unsolved Problems

21%

Aronszajn N., Gross L., Kwapień S., Nielsen N. J., Pełczyński A., Pietsch A., Schwartz L., Saphar P., Chevet S., Dudley R., Garling D. J. H., Kalton N. J., Mitjagin B., Rolewicz S., Schock E., Daleckiĭ J., Dobrakov J., Gelbaum B., Henkin G., Nachbin L., Peck N. T., Waelbroeck L., Porcelli P., Rao M. M., Zerner M., Zakharjuta V.

Studia Mathematica

|

1970

|

tom 38

|

nr 1

467-483

EN

1. The operator ideals and measures in linear spaces 469-472 2. Schauder bases and linear topological invariants 473-478 3. Various problems 479-483

16

Short Summaries

18%

Chevet S., Wojtyński W., Bessaga C., McCarthy C., Przeworska-Rolewicz D., Tomczak N., Mlak W., Persson A., Schlotterbeck U., Schmets J., Vladimirskiĭ Y. N., Szlenk W., Fenske C., Schock E., Kalton N. J., Gross L., Köthe G., Zerner M., Pytlik T., Skordev D., Peck N. T., de Wilde M., Szczyrba W., Neubauer G., Aronszajn N., Dennler G., Dobrakov I., Jonac M. L., Samuel C., Kōmura Y., Dragilev M. M., Semenov E. M., Popa N., Teleman S.

Studia Mathematica

|

1970

|

tom 38

|

nr 1

437-466

XX

S. CHEVET, p-ellipsoïdes de $l^{2}$. Mesures cylindriques gaussiennes 439-441 W. WOJTYŃSKI On conditional bases in non-nuclear Fréchet spaces 441 C. BESSAGA, A theorem on complemented subspaces of nuclear spaces 441-442 C. MCCARTHY, Optimal conditioning of operators 442-443 D. PRZEWORSKA-ROLEWICZ, On algebraic derivative 443-444 N. TOMCZAK, A remark (p,q)-absolutely summing operators in $L_{p}$-spaces 444-445 W. MLAK, Decompositions of operator representations of function algebras 445-446 A. PERSSON, p-integral operators 446-447 U. SCHLOTTERBECK, Elementary characterization of operators with absolutely summing adjoint 447 J. SCHMETS, Modulus of prenuclear maps in ordered spaces 447-448 Yu. N. VLADIMIRSKIĬ, On strictly cosingular operators in locally convex spaces 448-449 W. SZLENK, On weakly convergent sequences in Banach spaces 449-450 C. FENSKE, E. SCHOCK, Nuclearity and local convexity of sequence spaces 450-451 N. J. KALTON, The normalization of Schauder bases of locally convex spaces 451 L. GROSS, Nuclear operators and potential theory on Hilbert space 451-452 G. KÖTHE, On the structure of nuclear spaces 452 M. ZERNER, Développement en série de polynômes orthogonaux des fonctions indéfiniment différentiables 453 T. PYTLIK, A nuclear space of functions on a locally compact group 453-454 E. SCHOCK, Montel spaces of Hölder continuous functions 454 D. SKORDEV, Linear operators with sufficiently many a priori given eigenvectors 455-456 N. T. PECK, Some questions concerning support points 456 M. DE WILDE, On the equivalence of weak and Schauder basis 457 W. SZCZYRBA, On differentiability in some class of locally convex spaces 458 G. NEUBAUER, Fredholm links and perturbation theorems 459 N. ARONSZAJN, On finite-dimensional perturbations 459 G. DENNLER, Unbeschränkt teilbare zufällige Elemente in $L^{p}$-Räumen 459 G. DENNLER, Streng unabhängige Distributionen 460 I. DOBRAKOV, A representation theorem for unconditionally converging linear operators on $C_{0}(T,X)$ 460-461 M. L. JONAC, C. SAMUEL, Sur les espaces complementés de C(S) 461-462 Y. KŌMURA, Die Nuklearität der Lösungsräume der partiellen Differentialgleichungen 462-463 M. M. DRAGILEV, On certain topological invariants of Köthe spaces 463 E. M. SEMENOV, Interpolation of linear operators and its applications 463-464 N. POPA, Sur les produits tensoriels ordonnés 465 S. TELEMAN, Representation of finite von Neumann algebras by sheaves 465-466

Ograniczanie wyników

On vector-valued inequalities for Sidon sets and sets of interpolation

A note on galbed spaces

Calderón couples of rearrangement invariant spaces

Uniqueness of unconditional bases in $c_0$-products

A remark on a problem of Klee

Unconditional ideals in Banach spaces

Analytic functions in non-locally convex spaces and applications

Bases and basic sequences in F-spaces

Plurisubharmonic functions on quasi-Banach spaces

On operators on $L_0$

Schauder bases and reflexivity

Unconditional and normalised bases

Universal spaces and universal bases in metric spaces

Quotients of $L_{p}(0,1)$ for 0 ≤ p < 1

Unsolved Problems

Short Summaries