Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

6 Issues per year


IMPACT FACTOR 2017: 0.314
5-year IMPACT FACTOR: 0.462

CiteScore 2017: 0.46

SCImago Journal Rank (SJR) 2017: 0.339
Source Normalized Impact per Paper (SNIP) 2017: 0.845

Mathematical Citation Quotient (MCQ) 2017: 0.26

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 68, Issue 2

Issues

Skew-symmetric operators and reflexivity

Chafiq Benhida / Kamila Kliś-Garlicka / Marek Ptak
  • Department of Applied Mathematics University of Agriculture Balicka 253c 30-198 Krakow Poland
  • Institut of Mathematics Pedagogical University ul. Podchorążych 2 30-084 Kraków Poland
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-03-31 | DOI: https://doi.org/10.1515/ms-2017-0112

Abstract

In contrast to the subspaces of all C-symmetric operators, we show that the subspaces of all skew-C symmetric operators are reflexive and even hyperreflexive with the constant κ(𝓒s)≤ 3.

MSC 2010: Primary 47A15; Secondary 47L05

Keywords: skew-C symmetry; C-symmetry; reflexivity; hyperreflexivity

The first named author was partially supported by Labex CEMPI (ANR-11-LABX-0007-01). The research of the second and the third author was financed by the Ministry of Science and Higher Education of the Republic of Poland.

References

  • [1]

    Arveson, W. T.: Interpolation problems in nest algebras, J. Funct. Anal. 20 (1975), 208–233.CrossrefGoogle Scholar

  • [2]

    Garcia, S. R.—Putinar, M.: Complex symmetric operators and applications, Trans. Amer. Math. Soc. 358 (2006), 1285–1315.Google Scholar

  • [3]

    Garcia, S. R.—Putinar, M.: Complex symmetric operators and applications II, Trans. Amer. Math. Soc. 359 (2007), 3913–3931.CrossrefGoogle Scholar

  • [4]

    Garcia, S. R.—Wogen, W. R.: Some new classes of complex symmetric operators, Trans. Amer. Math. Soc. 362 (2010), 6065–6077.CrossrefGoogle Scholar

  • [5]

    Kliś-Garlicka, K.—Ptak, M.: C-symmetric operators and reflexivity, Oper. Matrices 9 (2015), 225–232.Web of ScienceGoogle Scholar

  • [6]

    Kliś, K.—Ptak, M.: k-hyperreflexive subspaces, Houston J. Math. 32 (2006), 299–313.Google Scholar

  • [7]

    Li, C. G.—Zhu, S.: Skew symmetric normal operators, Proc. Amer. Math. Soc. 141 (2013), 2755–2762.Web of ScienceCrossrefGoogle Scholar

  • [8]

    Loginov, A. I.—Shul’man, V. S.: Hereditary and intermediate reflexivity of W*-algebras, Izv. Akad. Nauk. SSSR 39 (1975), 1260–1273; Math. USSR-Izv. 9 (1975), 1189–1201.Google Scholar

  • [9]

    Sarason, D.: Algebraic properties of truncated Toeplitz operators, Oper. Matrices 1 (2007), 491–526.Web of ScienceGoogle Scholar

  • [10]

    Sarason, D.: Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1966), 511–517.CrossrefGoogle Scholar

  • [11]

    Zhu, S.: Skew symmetric weighted shifts, Banach J. Math. Anal. 9 (2015), 253–272.Web of ScienceCrossrefGoogle Scholar

  • [12]

    Zhu, S.: Approximate unitary equivalence to skew symmetric operators, Complex Anal. Oper. Theory 8 (2014), 1565–1580.CrossrefWeb of ScienceGoogle Scholar

About the article


Received: 2016-03-07

Accepted: 2016-05-14

Published Online: 2018-03-31

Published in Print: 2018-04-25


Citation Information: Mathematica Slovaca, Volume 68, Issue 2, Pages 415–420, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0112.

Export Citation

© 2018 Mathematical Institute Slovak Academy of Sciences.Get Permission

Comments (0)

Please log in or register to comment.
Log in