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Winter 2019 Some approximation properties and nuclear operators in spaces of analytical functions
Sten Kaijser, Oleg I‎. ‎Reinov
Adv. Oper. Theory 4(1): 265-283 (Winter 2019). DOI: 10.15352/aot.1805-1360

Abstract

‎‎We introduce and investigate a new notion of the approximation property $AP_{[c]},$‎ ‎where $c= (c_n)$ is an arbitrary positive real sequence‎, ‎tending to infinity‎. ‎Also‎, ‎we study the corresponding notion of $[c]$-nuclear operators in Banach spaces‎. ‎Some characterization of the $AP_{[c]}$ in terms of tensor products‎, ‎as well as‎ ‎sufficient conditions for a Banach space to have the $AP_{[c]},$ are given‎. ‎We give also sufficient conditions for a positive answer to the question‎: ‎When it follows from the $[c]$-nuclearity of an adjoint operator the nuclearity of‎ ‎the operator itself‎. ‎Obtained results are applied then to the study of properties‎ ‎of nuclear operators in some spaces of analytical functions‎. ‎Many examples are given‎.

Citation

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Sten Kaijser. Oleg I‎. ‎Reinov. "Some approximation properties and nuclear operators in spaces of analytical functions." Adv. Oper. Theory 4 (1) 265 - 283, Winter 2019. https://doi.org/10.15352/aot.1805-1360

Information

Received: 1 May 2018; Accepted: 25 August 2018; Published: Winter 2019
First available in Project Euclid: 20 September 2018

zbMATH: 06946454
MathSciNet: MR3867345
Digital Object Identifier: 10.15352/aot.1805-1360

Subjects:
Primary: 46B28
Secondary: ‎46E15

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 1 • Winter 2019
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