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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2024 Volume 65, Number 2, Pages 277–287 (Mi smj7854)

On the $K$-functionals of absolutely Calderón elements of the Banach pair $( l_{1} , c_{0} )$

V. I. Dmitrieva, E. V. Zhuravlevaa, O. Yu. Mikhailovaa, I. N. Burilichb

a MIREA — Russian Technological University, Moscow
b Kursk State University

Abstract: We characterize the absolutely Calderón elements of the canonical pair $(l_1, c_0)$ of sequence spaces in terms of the Peetre $K$-functional. This result has been known to the first author since rather long ago but the proof appears here. Also, we formulate a few unsolved problems.

Keywords: Banach pair, interpolation orbit, Peetre K-functional.

UDC: 513.88

MSC: 35R30

Received: 10.07.2023
Revised: 12.12.2023
Accepted: 28.01.2024

DOI: 10.33048/smzh.2024.65.204



© Steklov Math. Inst. of RAS, 2024