WEAKLY COMPACT WEDGE OPERATORS ON KOTHE ECHELON SPACES
Abstract. We study wedge operators dened on spaces of operators between Kothe echelon or co-echelon spaces of order 1 < p < 1. In this case the wedge operator, dened by T! LTR for non-zero operators L and R, maps bounded sets into relatively weakly compact sets if and only if the operator L or...
| Main Authors: | , , , |
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| Format: | Text |
| Language: | English |
| Subjects: | |
| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.618.7546 http://emis.math.tifr.res.in/journals/AASF/Vol29/bonet.pdf |
| Summary: | Abstract. We study wedge operators dened on spaces of operators between Kothe echelon or co-echelon spaces of order 1 < p < 1. In this case the wedge operator, dened by T! LTR for non-zero operators L and R, maps bounded sets into relatively weakly compact sets if and only if the operator L or the operator R maps bounded sets into relatively compact sets. This is an extension of a result of Saksman and Tylli for the sequence space lp. The corresponding result for operators mapping a neighbourhood into a relatively weakly compact set does not hold, as an example shows. 1. Introduction and |
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