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On Zd-symmetry of spectra of some nuclear operators. / Reinov, Oleg I,.

Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov. ed. / P.Kurasov; A.Laptev; S.Naboko; B.Simon. Birkhäuser, Cham : Springer Nature, 2020. p. 554-569 (Operator Theory: Advances and Applications; Vol. 276).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Harvard

Reinov, OI 2020, On Zd-symmetry of spectra of some nuclear operators. in P.Kurasov, A.Laptev, S.Naboko & B.Simon (eds), Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov. Operator Theory: Advances and Applications, vol. 276, Springer Nature, Birkhäuser, Cham, pp. 554-569, Spectral Theory and Applications, Stockholm, Sweden, 13/03/16. https://doi.org/10.1007/978-3-030-31531-3_29

APA

Reinov, O. I. (2020). On Zd-symmetry of spectra of some nuclear operators. In P.Kurasov, A.Laptev, S.Naboko, & B.Simon (Eds.), Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov (pp. 554-569). (Operator Theory: Advances and Applications; Vol. 276). Springer Nature. https://doi.org/10.1007/978-3-030-31531-3_29

Vancouver

Reinov OI. On Zd-symmetry of spectra of some nuclear operators. In P.Kurasov, A.Laptev, S.Naboko, B.Simon, editors, Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov. Birkhäuser, Cham: Springer Nature. 2020. p. 554-569. (Operator Theory: Advances and Applications). https://doi.org/10.1007/978-3-030-31531-3_29

Author

Reinov, Oleg I,. / On Zd-symmetry of spectra of some nuclear operators. Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov. editor / P.Kurasov ; A.Laptev ; S.Naboko ; B.Simon. Birkhäuser, Cham : Springer Nature, 2020. pp. 554-569 (Operator Theory: Advances and Applications).

BibTeX

@inproceedings{7ed224e26ca24aad846d9f2594faba25,
title = "On Zd-symmetry of spectra of some nuclear operators",
abstract = "It was shown by M. I. Zelikin (2007) that the spectrum of a nuclearoperator in a Hilbert space is central-symmetric i the traces of all odd powersof the operator equal zero. B. Mityagin (2016) generalized Zelikin's criteriumto the case of compact operators (in Banach spaces) some of which powers arenuclear, considering even a notion of so-called Zd-symmetry of spectra introducedby him. We study α-nuclear operators generated by the tensor elements of socalled α-projective tensor products of Banach spaces, introduced in the paper (αis a quasi-norm). We give exact generalizations of Zelikin's theorem to the casesof Zd-symmetry of spectra of α-nuclear operators (in particular, for s-nuclear andfor (r, p)-nuclear operators). We show that the results are optimal.",
keywords = "eigenvalue, approximation property, tensor product, Nuclear operator",
author = "Reinov, {Oleg I,}",
note = "Reinov, O. (2020). On Zd -symmetry of spectra of some nuclear operators. In: Kurasov, P., Laptev, A., Naboko, S., Simon, B. (eds) Analysis as a Tool in Mathematical Physics. Operator Theory: Advances and Applications, vol 276. Birkh{\"a}user, Cham. https://doi.org/10.1007/978-3-030-31531-3_29; null ; Conference date: 13-03-2016 Through 15-03-2016",
year = "2020",
month = jul,
day = "1",
doi = "10.1007/978-3-030-31531-3_29",
language = "English",
isbn = "97830303155306",
series = "Operator Theory: Advances and Applications",
publisher = "Springer Nature",
pages = "554--569",
editor = "P.Kurasov and A.Laptev and S.Naboko and B.Simon",
booktitle = "Analysis as a Tool in Mathematical Physics",
address = "Germany",
url = "http://staff.math.su.se/kurasov/SpectralTheory2016/index.html",

}

RIS

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T1 - On Zd-symmetry of spectra of some nuclear operators

AU - Reinov, Oleg I,

N1 - Reinov, O. (2020). On Zd -symmetry of spectra of some nuclear operators. In: Kurasov, P., Laptev, A., Naboko, S., Simon, B. (eds) Analysis as a Tool in Mathematical Physics. Operator Theory: Advances and Applications, vol 276. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-31531-3_29

PY - 2020/7/1

Y1 - 2020/7/1

N2 - It was shown by M. I. Zelikin (2007) that the spectrum of a nuclearoperator in a Hilbert space is central-symmetric i the traces of all odd powersof the operator equal zero. B. Mityagin (2016) generalized Zelikin's criteriumto the case of compact operators (in Banach spaces) some of which powers arenuclear, considering even a notion of so-called Zd-symmetry of spectra introducedby him. We study α-nuclear operators generated by the tensor elements of socalled α-projective tensor products of Banach spaces, introduced in the paper (αis a quasi-norm). We give exact generalizations of Zelikin's theorem to the casesof Zd-symmetry of spectra of α-nuclear operators (in particular, for s-nuclear andfor (r, p)-nuclear operators). We show that the results are optimal.

AB - It was shown by M. I. Zelikin (2007) that the spectrum of a nuclearoperator in a Hilbert space is central-symmetric i the traces of all odd powersof the operator equal zero. B. Mityagin (2016) generalized Zelikin's criteriumto the case of compact operators (in Banach spaces) some of which powers arenuclear, considering even a notion of so-called Zd-symmetry of spectra introducedby him. We study α-nuclear operators generated by the tensor elements of socalled α-projective tensor products of Banach spaces, introduced in the paper (αis a quasi-norm). We give exact generalizations of Zelikin's theorem to the casesof Zd-symmetry of spectra of α-nuclear operators (in particular, for s-nuclear andfor (r, p)-nuclear operators). We show that the results are optimal.

KW - eigenvalue

KW - approximation property

KW - tensor product

KW - Nuclear operator

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U2 - 10.1007/978-3-030-31531-3_29

DO - 10.1007/978-3-030-31531-3_29

M3 - Conference contribution

AN - SCOPUS:85088587514

SN - 97830303155306

T3 - Operator Theory: Advances and Applications

SP - 554

EP - 569

BT - Analysis as a Tool in Mathematical Physics

A2 - P.Kurasov, null

A2 - A.Laptev, null

A2 - S.Naboko,

A2 - B.Simon,

PB - Springer Nature

CY - Birkhäuser, Cham

Y2 - 13 March 2016 through 15 March 2016

ER -

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