scholarly journals Lower bounds for matrices on block weighted sequence spaces I

2009 ◽  
Vol 59 (1) ◽  
pp. 81-94 ◽  
Author(s):  
R. Lashkaripour ◽  
D. Foroutannia
Keyword(s):  
Lower Bounds ◽  
Sequence Spaces ◽  
Weighted Sequence

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.

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