Operator valued series, almost summability of vector valued multipliers and (weak) compactness of summing operator

2020 ◽  
Vol 484 (1) ◽  
pp. 123651 ◽  
Author(s):  
Mahmut Karakuş ◽  
Feyzi Başar
Keyword(s):  
Weak Compactness ◽  
Summing Operator ◽  
Vector Valued

scholarly journals Weak compactness in spaces of vector valued measures

1988 ◽  
Vol 38 (1) ◽  
pp. 55-56
Author(s):  
F.G.J. Wiid
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Weak Compactness ◽  
Vector Valued

We characterise relative weak compactness in σBM(∑, X), the space of sigma-additive, X-valued measures of bounded variation, where X is a Banach space.

scholarly journals Characterizations of vector-valued weakly almost periodic functions

2003 ◽  
Vol 2003 (5) ◽  
pp. 295-304
Author(s):  
Chuanyi Zhang
Keyword(s):  
Continuous Function ◽  
Weak Compactness ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Weakly Compact ◽  
Bounded Continuous Function ◽  
Weakly Almost Periodic ◽  
Equivalent Properties ◽  
Vector Valued

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties.

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