Standard

Some approximation properties and nuclear operators in spaces of analytical functions. / Kaijser, Sten; Reinov, Oleg I.

In: Advances in Operator Theory, Vol. 4, No. 1, 01.2019, p. 265-283.

Research output: Contribution to journal › Article › peer-review

Harvard

Kaijser, S & Reinov, OI 2019, 'Some approximation properties and nuclear operators in spaces of analytical functions', Advances in Operator Theory, vol. 4, no. 1, pp. 265-283. https://doi.org/10.15352/aot.1805-1360

APA

Kaijser, S., & Reinov, O. I. (2019). Some approximation properties and nuclear operators in spaces of analytical functions. Advances in Operator Theory, 4(1), 265-283. https://doi.org/10.15352/aot.1805-1360

Vancouver

Kaijser S, Reinov OI. Some approximation properties and nuclear operators in spaces of analytical functions. Advances in Operator Theory. 2019 Jan;4(1):265-283. https://doi.org/10.15352/aot.1805-1360

Author

Kaijser, Sten ; Reinov, Oleg I. / Some approximation properties and nuclear operators in spaces of analytical functions. In: Advances in Operator Theory. 2019 ; Vol. 4, No. 1. pp. 265-283.

BibTeX

@article{6d7a4f8ac519416e81e6398d88b3f1eb,
title = "Some approximation properties and nuclear operators in spaces of analytical functions",
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. ",
keywords = "Approximation property, Nuclear operator, Space of bounded analytical functions, Tensor product",
author = "Sten Kaijser and Reinov, {Oleg I.}",
note = "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. https://projecteuclid.org/euclid.aot/1537408976",
year = "2019",
month = jan,
doi = "10.15352/aot.1805-1360",
language = "English",
volume = "4",
pages = "265--283",
journal = "Advances in Operator Theory",
issn = "2538-225X",
publisher = "Tusi Mathematical Research Group",
number = "1",

}

RIS

TY - JOUR

T1 - Some approximation properties and nuclear operators in spaces of analytical functions

AU - Kaijser, Sten

AU - Reinov, Oleg I.

N1 - 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. https://projecteuclid.org/euclid.aot/1537408976

PY - 2019/1

Y1 - 2019/1

N2 - 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.

AB - 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.

KW - Approximation property

KW - Nuclear operator

KW - Space of bounded analytical functions

KW - Tensor product

UR - http://www.aot-math.org/article_67535.html

UR - http://www.scopus.com/inward/record.url?scp=85056588013&partnerID=8YFLogxK

U2 - 10.15352/aot.1805-1360

DO - 10.15352/aot.1805-1360

M3 - Article

VL - 4

SP - 265

EP - 283

JO - Advances in Operator Theory

JF - Advances in Operator Theory

SN - 2538-225X

IS - 1

ER -

ID: 30499902