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1993 | 104 | 1 | 99-110
Tytuł artykułu

Trace inequalities for spaces in spectral duality

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EN
Abstrakty
EN
Let (A,e) and (V,K) be an order-unit space and a base-norm space in spectral duality, as in noncommutative spectral theory of Alfsen and Shultz. Let t be a norm lower semicontinuous trace on A, and let φ be a nonnegative convex function on ℝ. It is shown that the mapping a → t(φ(a)) is convex on A. Moreover, the mapping is shown to be nondecreasing if so is φ. Some other similar statements concerning traces and real-valued functions are also obtained.
Słowa kluczowe
Czasopismo
Rocznik
Tom
104
Numer
1
Strony
99-110
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-06-30
Twórcy
  • Research Institute of Mathematics and Mechanics, Kazan University, Lenin Str. 18, Kazan 420008, Russian Federation.
Bibliografia
  • [1] S. A. Ajupov, Extension of traces and type criterions for Jordan algebras of self-adjoint operators, Math. Z. 181 (1982), 253-268.
  • [2] E. M. Alfsen, Compact Convex Sets and Boundary Integrals, Ergeb. Math. Grenzgeb. 57, Springer, Berlin 1971.
  • [3] E. M. Alfsen and F. W. Shultz, Non-commutative spectral theory for affine function spaces on convex sets, Mem. Amer. Math. Soc. 172 (1976).
  • [4] M. A. Berdikulov, Traces on Jordan algebras, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk 1986 (3), 11-15 (in Russian).
  • [5] F. A. Berezin, Convex operator functions, Mat. Sb. 88 (1972), 268-276 (in Russian).
  • [6] L. G. Brown and H. Kosaki, Jensen's inequality in semi-finite von Neumann algebras, J. Operator Theory 23 (1990), 3-19.
  • [7] T. Fack and H. Kosaki, Generalized s-numbers of τ-measurable operators, Pacific J. Math. 123 (1986), 269-300.
  • [8] A. Lieberman, Entropy of states of a gage space, Acta Sci. Math. (Szeged) 40 (1978), 99-105.
  • [9] D. Petz, Spectral scale of self-adjoint operators and trace inequalities, J. Math. Anal. Appl. 109 (1985), 74-82.
  • [10] D. Petz, Jensen's inequality for positive contractions on operator algebras, Proc. Amer. Math. Soc. 99 (1987), 273-277.
  • [11] O. E. Tikhonov, Inequalities for a trace on a von Neumann algebra, VINITI, Moscow 1982, No. 5602-82 (in Russian).
  • [12] O. E. Tikhonov, Convex functions and inequalities for traces, in: Konstr. Teor. Funktsiĭ i Funktsional. Anal. 6, Kazan Univ. 1987, 77-82 (in Russian).
  • [13] O. E. Tikhonov, Inequalities for spaces in spectral duality, connected with convex functions and traces, VINITI, Moscow 1987, No. 3591-B87 (in Russian).
  • [14] O. E. Tikhonov, On integration theory for spaces in spectral duality, in: Proc. 1st Winter School on Measure Theory (Liptovský Ján 1988), Slovak Acad. Sci., Bratislava 1988, 157-160.
  • [15] H. Upmeier, Automorphism groups of Jordan C*-algebras, Math. Z. 176 (1981), 21-34.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv104i1p99bwm
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