Powiadomienia systemowe
- Sesja wygasła!
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Given Hilbert space operators T, S ∈ B(H), let Δ and δ ∈ B(B (H)) denote the elementary operators ΔT,S(X) = (LT RS − I) (X) = TXS - X and δT,S(X) = (LT – RS)(X) = TX - XS. Let d = Δ or δ. Assuming T commutes with S∗, and choosing X to be the positive operator S∗nSn for some positive integer n, this paper exploits properties of elementary operators to study the structure of n-quasi [m, d]-operators dm T,S (X) = 0 to bring together, and improve upon, extant results for a number of classes of operators, such as n-quasi left m-invertible operators, n-quasi m-isometric operators, n-quasi m-self-adjoint operators and n-quasi (m, C) symmetric operators (for some conjugation C of H). It is proved that Sn is the perturbation by a nilpotent of the direct sum of an operator Sn1 = (…)n satisfying dmT1S1(I1) = 0 , T1 = (…) , with the 0 operator; if S is also left invertible, then Sn is similar to an operator B such that dmB∗,B(I) = 0. For power bounded S and T such that ST∗ - T∗S = 0 and ΔTS(S∗nSn) = 0, S is polaroid (i.e., isolated points of the spectrum are poles). The product property, and the perturbation by a commuting nilpotent property, of operators T, S satisfying dmT,S (I) = 0, given certain commutativity properties, transfers to operators satisfying S∗ndmT,S (I)Sn = 0.
Wydawca
Czasopismo
Rocznik
Tom
Strony
249--268
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Mathematics, Loosely attached to Nis Univ. in Nis (Serbia), 8 Redwood Grove, Northfields Avenue, Ealing, London, W5 4SZ, England, United Kingdom
autor
- Department of Mathematics, Incheon National University, Incheon, 406-772, Korea
Bibliografia
- [1] O. A. M. Sid Ahmed, Some properties of m-isometries and m-invertible operators in Banach spaces, Acta Math. Sci. Ser. B English Ed. 32(2012), 520-530.
- [2] B. P. Duggal and V. Müller, Tensor product of left n-invertible operators, Studia Math. 215(2013), no. 2, 113–125.
- [3] C. Gu, Structure of left n-invertible operators and their applications, Studia Math. 226(2015), 189–211.
- [4] J. Agler and M. Stankus, m-isometric transformations of Hilbert space I, Integr. Equat. Oper. Theory 21(1995), 383–420.
- [5] T. Bermûdez, A. Martinón, V. Müller, and J. N. Noda, Perturbation of m-isometries by nilpotent operators, Abstr. Appl. Anal. 2014(2014), 745479, DOI: 10.1155/2014/745479.
- [6] B. P. Duggal, Tensor product of n-isometries III, Funct. Anal. Approx. Comput. 4(2012), no. 2, 61–67.
- [7] T. Le, Algebraic properties of operator roots of polynomials, J. Math. Anal. Appl. 421(2015), no. 2, 1238–1246.
- [8] M. Chō, E. Ko, and J. E. Lee, On (m,C)-isometric operators, Complex Anal. Oper. Theory 10(2016), 1679–1694, DOI: 10.1007/s11785-016-0549-0.
- [9] M. Chō, J. E. Lee, and H. Motoyoshi, On [m,C]-isometric operators, Filomat 31(2017), no. 7, 2073–2080, DOI: 10.2307/26194944.
- [10] S. Mecheri and S. M. Patel, On quasi 2-isometric operators, Linear Multilinear Algebra 66(2018), no. 5, 1019–1025, DOI: 10.1080/03081087.2017.1335283.
- [11] O. A. M. Sid Ahmed, M. Chō, and J. E. Lee, On n-quasi-(m,C)-isometric operators, Linear Multilinear Algebra 68(2020), no. 5, 1001–1020, DOI: 10.1080/03081087.2018.1524437.
- [12] I. H. Kim, On (p,k)-quasihyponormal operators, Math. Inequal. Appl. 7(2004), 629–638.
- [13] P. Aiena, Fredholm and Local Spectral Theory, with Applications to Multipliers, Kluwer Academic Publishers, New York, Boston, Dordrecht, London, Moscow, 2004.
- [14] H. G. Heuser, Functional Analysis, John Wiley and Sons, Chicester, New York, Brisbane, Toronto, Singapore, 1982.
- [15] K. B. Laursen and M. N. Neumann, Introduction to Local Spectral Theory, Clarendon Press, Oxford, 2000.
- [16] A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, John Wiley and Sons, New York, 1980.
- [17] B. P. Duggal, Hereditarily normaloid operators, Extracta Math. 20(2005), no. 2, 203–217.
- [18] L. Suciu and N. Suciu, Ergodic conditions and spectral properties for A-contractions, Opscula Math. 28(2008), 195–216.
- [19] P. R. Halmos, A Hilbert Space Problem Book, 2nd edn, Springer, New York, 1982.
- [20] D. Koehler and P. Rosenthal, On isometries of normed linear spaces, Studia Math. 36(1970), 213–216.
- [21] B. P. Duggal and C. S. Kubrusly, Power bounded left m-invertible operators, Linear Multilinear Algebra (2019), DOI: 10.1080/03081087.2019.1604623.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-62889111-eb25-44b2-9454-1e6bed26ef8f