Advances in Operator Theory

Some approximation properties and nuclear operators in spaces of analytical functions

Sten Kaijser and Oleg I‎. ‎Reinov

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‎‎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.

Article information

Adv. Oper. Theory, Volume 4, Number 1 (2019), 265-283.

Received: 1 May 2018
Accepted: 25 August 2018
First available in Project Euclid: 20 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions

nuclear operator‎ ‎tensor product‎ ‎approximation property‎‎ ‎space of bounded analytical functions


Kaijser, Sten; ‎Reinov, Oleg I‎. Some approximation properties and nuclear operators in spaces of analytical functions. Adv. Oper. Theory 4 (2019), no. 1, 265--283. doi:10.15352/aot.1805-1360.

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