2-local isometries of non-commutative Lorentz spaces

Автор: Alimov Akrom A., Chilin Vladimir I.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 4 т.21, 2019 года.

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Let M be a von Neumann algebra equipped with a faithful normal finite trace τ, and let S(M,τ) be an ∗-algebra of all τ-measurable operators affiliated with M. For x∈S(M,τ) the generalized singular value function μ(x):t→μ(t;x), t>0, is defined by the equality μ(t;x)=inf{∥xp∥M:p2=p∗=p∈M,τ(1-p)≤t}. Let ψ be an increasing concave continuous function on [0,∞) with ψ(0)=0, ψ(∞)=∞, and let Λψ(M,τ)={x∈S(M,τ): ∥x∥ψ=∫∞0μ(t;x)dψ(t)

Measurable operator, lorentz space, isometry

Короткий адрес: https://readera.org/143168813

IDR: 143168813   |   DOI: 10.23671/VNC.2019.21.44595

Список литературы 2-local isometries of non-commutative Lorentz spaces

  • Aminov, B. R. and Chilin, V. I. Isometries of Perfect Norm Ideals of Compact Operators, Studia Mathematica, 2018, vol. 241, no. 1, pp. 87-99. DOI: 10.4064/sm170306-19-4
  • Molnar, L. 2-Local Isometries of some Operator Algebras, Proceedings of the Edinburgh Mathematical Society, 2002, vol. 45, pp. 349-352. DOI: 10.1017/S0013091500000043
  • Sourour, A. Isometries of Norm Ideals of Compact Operators, Journal of Functional Analysis, 1981, vol. 43, no. 1, pp. 69-77. DOI: 10.1016/0022-1236(81)90038-0
  • Lord, S., Sukochev, F. and Zanin, D. Singular Traces. Theory and Applications, Berlin/Boston, Walter de Gruyter GmbH, 2013.
  • Chilin, V. I., Medzhitov, A. M. and Sukochev, F. A. Isometries of Non-Commutative Lorentz Spaces, Mathematische Zeitschrift, 1989, vol. 200, no. 4, pp. 527-545. DOI: 10.1007/BF01160954
  • Takesaki, M. Theory of Operator Algebras I, New York, Springer-Verlag, 1979.
  • Fack, T. and Kosaki, H. Generalized s-Numbers of τ-Measurable Operators, Pacific Journal of Mathematics, 1986, vol. 123, no. 2, pp. 269-300.
  • DOI: 10.2140/pjm.1986.123.269
  • Chilin, V. I. and Sukochev, F. A. Weak Convergence in Non-Commutative Symmetric Spaces, Journal of Operator Theory, 1994, vol. 31, no. 1, pp. 35-55.
  • Ciach, L. J. On the Conjugates of Some Operator Spaces, I, Demonstratio Mathematica, 1985, vol. 18, no. 2, pp. 537-554.
  • DOI: 10.1515/dema-1985-0213
  • Bratteli, O. and Robinson, D. W. Operator Algebras and Quantum Statistical Mechaniks, N.Y.-Heidelber-Berlin, Springer-Verlag, 1979.
  • Sarymsakov, T. A., Ayupov, Sh. A., Khadzhiev D. and Chilin V. I. Uporyadochennye Algebry [Ordered Algebras], Tashkent, FAN, 1983 [in Russian].
  • Fleming, R. J., Jamison, J. E. Isometries on Banach Spaces: Function Spaces, Florida, Boca Raton, Chapman-Hall/CRC, 2003.
  • Krein, M. G., Petunin, Ju. I. and Semenov, E. M. Interpolation of Linear Operators, Translations of Mathematical Monographs, vol. 54, American Mathematical Society, 1982.
  • Dodds, P., Dodds. Th. K.-Y and Pagter, B. Noncommutative Kothe Duality, Transactions of the American Mathematical Society, 1993, vol. 339, no. 2, pp. 717-750.
  • DOI: 10.1090/S0002-9947-1993-1113694-3
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