Unconditional bases in Fr�chet-spaces

1986 ◽  
Vol 47 (2) ◽  
pp. 129-130 ◽  
Author(s):  
Klaus Floret ◽  
Vincenzo Bruno Moscatelli
Keyword(s):  
Unconditional Bases

scholarly journals Compact diagonal linear operators on Banach spaces with unconditional bases

1993 ◽  
Vol 16 (4) ◽  
pp. 823-824
Author(s):  
Yun Sung Choi ◽  
Sung Guen Kim
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Uniform Continuity ◽  
Linear Operators ◽  
Unconditional Bases

LetEandFbe Banach spaces with equivalent normalized unconditional bases. In this note we show that a bounded diagonal linear operatorT:E→Fis compact if and only if its entries tend to0, using the concept of weak uniform continuity.

scholarly journals Wavelets Convergence and Unconditional Bases for Lp(ℝn) and H1(ℝn)

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Devendra Kumar
Keyword(s):  
Banach Space ◽  
Hardy Space ◽  
Function Space ◽  
Riesz Transform ◽  
Unconditional Bases

We prove that reasonable nice wavelets form unconditional bases in function space other than L2(ℝn, X). Moreover, characterization of convergence of wavelets series in Lp(ℝn, X) space and Hardy space H1(ℝn,X) has been obtained. Here, X is a Banach space with boundedness of Riesz transform.

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