• Nie Znaleziono Wyników

# Abstract. It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X

N/A
N/A
Protected

Share "Abstract. It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X"

Copied!
10
0
0
Pokaż więcej ( Stron)

Pełen tekst

(1)

+

n

n

n1

1

2

n

[193]

(2)

n

1

2

n1

n2

n

n

n

m

n

n

n

n

1

k

(3)

n

n

k

+

+

n

n

n

n

0

Φ

0

Φ

i=1

i

Φ

Φ

0

Φ

Φ

Φ

Φ

Φ

Φ

Φ

(4)

2

2

0

i

i=1

i

i

i

i

0

Φ

Φ

2

i

i

i

i

2

Φ

i

i

2

Φ

Φ

Φ

Φ

i

2

i

i=1

i

i

i

i

i

i

i

n

1

2

n1

n2

n

0

n

n

(5)

n

0.

0

k

1

1

k(1)

n

n

n

1

k

0

1

0

k

0

1

k

1

0

k

0

k

0

0

0

0

1

0

1

i

i

Φ

Φ

2

(6)

2

Φ

Φ

Φ

i

i

i+1

i

i

i+1

i

i

Φ

i

Φ

i

Φ

0

1

0

1

0

0

Ψ

1

Φ

0

0

Ψ

i=1

i

0

i

1

i

i

0

ni+1

j=ni+1

0

ni+1

j=ni+1

j

j

0

i

Φ

Φ

2

0

n

Φ

n

0

n

n

0

n

0

2

0

Φ

n

0

Φ

0

2

0

0

Φ

Φ

0

Φ

0

n

Φ

n

(7)

0

i=i0+1

i

0

n

n

0

i0

i=1

i

n

i0

i=1

i

0

i0

i=1

i

n

0

0

i=1

i

n

i0

i=1

i

n

i=i0+1

i

n

i0

i=1

i

0

i=i0+1

i

n

0

Φ

n

i=1

i

n

i0

i=1

i

n

i=i0+1

i

n

0

i=i0+1

i

n

0

i0

i=1

i

0

0

0

0

0

0

0

i

i

Φ

Φ

2

2

Φ

2

2

(pi)

Φ

i

i

pi

i

(pi)

(8)

(pi)

(pi)

i

i

i

i

i

i

pi

2

i

i

2

i

i

(pi)

(pi)

(pi)

i

i

i

i

pi

2

i

i

i

Φ

2

2

Φ

2

2

2

i

i=1

i

i

i

i

i

i

i

2

Φ

Φ

Φ

Φ

n

Φ

n

n

0

0

i=i0+1

i

1

i=i0+1

i

i

i0

i=1

i

n

0

i=i0+1

i

n

0

(9)

Φ

1

n

i0

i=1

i

n

1

i=i0+1

i

n

1

i0

i=1

i

1

i=i0+1

i

n

i0

i=1

i

1

i=i0+1

i

n

i=i0+1

i

i

i0

i=1

i

1

i=i0+1

i

n

i=i0+1

i

i

i=i0+1

i

n

0

1

n

1

n

0

(pi)

i

i

i

i

## < ∞.

p

(1)n

(10)

### R´evis´e le 25.6.1996

Cytaty

Powiązane dokumenty

Many papers on the weak convergence of iterates of asymptotically non- expansive mappings have appeared recently; their setting is either a uni- formly convex space with a

Media – Kultura – Komunikacja Społeczna 10/1,

W artykule zostały postawione dwa następujące pytania badawcze: jak wygląda demokracja bez narodu (tutaj na przykładzie demokracji na poziomie ponadnarodowym w UE)?, oraz jakie

aug(H % ), which is the closure of the class of all well- founded posets with antichain rank ≤ % under inversion, lexicographic sums, and augmentation, contains the class of

Next, we give some corollaries and some examples of 99 -functions with parameter, which generate uniformly convex Musielak — Orlicz spaces... I t is obvious that

“Banach–Saks property in some Banach sequence

Key words and phrases: absolute norm, convex function, ψ-direct sum of Banach spaces, weak nearly uniform smoothness, Garcia-Falset coefficient, Schur property, WORTH property,

UPOTP for continuous self-mappings of compact metric spaces was defined and two strong hypotheses were stated, namely the genericity of UPOTP in continuous self-mappings of

Moreover, these moduli are suitable for nearly uniformly convex spaces (N.U.C.) introduced in [H] in the same sense as the classical modulus of convexity of Clarkson is suitable

The motivation for this is that in the case of continued frac- tions, the asymptotic behaviour for the relevant sequence of digits was de- duced from the identification of the

Banach–Mazur distance, nearly (almost) isometric Banach spaces, ` 1 -preduals, hyperplanes in c, weak ∗ fixed point property, stable weak ∗ fixed point property, almost stable weak

Criteria for k-strict convexity, uniform convexity in every direction, prop- erty K, property H, and property G in Musielak-Orlicz sequence spaces and their subspaces endowed with

In this paper, we discuss Orlicz sequence spaces endowed with the Luxemburg norm, and get an interesting result that λ(l M ) may take every value in the harmonic number sequence {1/n}

As usual {u.a.p.} denotes the algebra of Bohr’s almost periodic functions i.e., the closure of the set A in the uniform norm of C b (R) (the space of continuous and bounded functions

In this paper, we present criteria for local uniform rotundity and weak local uniform rotundity in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm1. 2000

Hernández, Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040-Madrid, Spain ( e-mail: juanmanuel − hrl@hotmail.com)..

Suppose E is a Banach lattice and EA is order dense in E (for example, this holds in Orlicz spaces generated by finite-valued functions). The dual space E% can be

Complex extreme point, complex strict convexity and complex uniform convexity of complex Banach space are natural generalizations of extreme point, strict

Subsequently, Gul’ko conjectured that the Lindel¨ of property of all iterated continuous function spaces actually characterizes the class of Corson compacta (Problem 1052 in [11])..

cenił, potrafił nazwać „starą wariatką&#34; 1 2. Szacunkowi dla osób, instytucji i tradycji, miłości do ojczyzny i Kościoła towa- rzyszy więc w tej twórczości stale

Then, by standard arguments, there exist a weakly compact convex subset K of Y with diam(X) =1 and a fixed point free nonexpansive map T : K —&gt; K such that K is minimal for T

We prove that if (X ν ) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach–Saks property, then the deviation from the weak Banach–Saks property of an

Wybierz swój język

Strona internetowa zostanie przetłumaczona na wybrany język.

Proponowane języki dla Ciebie:

Inny: