On Pitt's Theorem for Operators between Scalar and Vector-Valued Quasi-Banach Sequence Spaces

2000 ◽  
Vol 130 (1) ◽  
pp. 7-18 ◽  
Author(s):  
A. Defant ◽  
J. A. López Molina ◽  
M. J. Rivera
Keyword(s):  
Sequence Spaces ◽  
Banach Sequence Spaces ◽  
Vector Valued ◽  
Banach Sequence ◽  
Pitt’S Theorem

ENTROPY NUMBERS OF DIAGONAL OPERATORS BETWEEN VECTOR-VALUED SEQUENCE SPACES

2001 ◽  
Vol 64 (3) ◽  
pp. 739-754 ◽  
Author(s):  
THOMAS KÜHN ◽  
TOMAS P. SCHONBEK
Keyword(s):  
Lower Bounds ◽  
Sequence Spaces ◽  
Upper And Lower Bounds ◽  
Entropy Numbers ◽  
Diagonal Operators ◽  
Weighted Sequence ◽  
Banach Sequence Spaces ◽  
Vector Valued ◽  
Banach Sequence

Upper and lower bounds are established for the entropy numbers of certain diagonal operators between Banach sequence spaces. These diagonal operators are isomorphisms between the spaces considered in the paper and weighted sequence spaces considered by Leopold so that the entropy numbers in question coincide with those considered by Leopold. The results in the paper improve the previous results in at least two ways. The estimates in the paper are ‘almost’ sharp in the sense that the upper and lower estimates differ only by logarithmic factors for a much wider range of parameters. Moreover, all the upper estimates are improvements on the previous ones, the improvement being quite significant in some cases.

Weak orthogonality and weak property (β) in some banach sequence spaces

1999 ◽  
Vol 49 (2) ◽  
pp. 303-316 ◽  
Author(s):  
Yunan Cui ◽  
Henryk Hudzik ◽  
Ryszard Płuciennik
Keyword(s):  
Sequence Spaces ◽  
Banach Sequence Spaces ◽  
Weak Property ◽  
Banach Sequence

scholarly journals On the Dvoretzky-Rogers theorem

1984 ◽  
Vol 27 (2) ◽  
pp. 105-113
Author(s):  
Fuensanta Andreu
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Sequence Spaces ◽  
Finite Dimensional ◽  
Banach Sequence Spaces ◽  
Perfect Sequence ◽  
Normal Topology ◽  
Banach Sequence

The classical Dvoretzky-Rogers theorem states that if E is a normed space for which l1(E)=l1{E} (or equivalently , then E is finite dimensional (see [12] p. 67). This property still holds for any lp (l<p<∞) in place of l1 (see [7]p. 104 and [2] Corollary 5.5). Recently it has been shown that this result remains true when one replaces l1 by any non nuclear perfect sequence space having the normal topology (see [14]). In this context, De Grande-De Kimpe [4] gives an extension of the Devoretzky-Rogers theorem for perfect Banach sequence spaces.

scholarly journals Banach-Saks Type and Gurariǐ Modulus of Convexity of Some Banach Sequence Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Henryk Hudzik ◽  
Vatan Karakaya ◽  
Mohammad Mursaleen ◽  
Necip Simsek
Keyword(s):  
Sequence Spaces ◽  
Modulus Of Convexity ◽  
Banach Sequence Spaces ◽  
Banach Sequence

Banach-Saks type is calculated for two types of Banach sequence spaces and Gurariǐ modulus of convexity is estimated from above for the spaces of one type among them.

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