# Trace inequalities for spaces in spectral duality

Studia Mathematica (1993)

- Volume: 104, Issue: 1, page 99-110
- ISSN: 0039-3223

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topTikhonov, O.. "Trace inequalities for spaces in spectral duality." Studia Mathematica 104.1 (1993): 99-110. <http://eudml.org/doc/215962>.

@article{Tikhonov1993,

abstract = {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.},

author = {Tikhonov, O.},

journal = {Studia Mathematica},

keywords = {order-unit space; base-norm space; spectral duality; noncommutative spectral theory of Alfsen and Shultz; norm lower semicontinuous trace},

language = {eng},

number = {1},

pages = {99-110},

title = {Trace inequalities for spaces in spectral duality},

url = {http://eudml.org/doc/215962},

volume = {104},

year = {1993},

}

TY - JOUR

AU - Tikhonov, O.

TI - Trace inequalities for spaces in spectral duality

JO - Studia Mathematica

PY - 1993

VL - 104

IS - 1

SP - 99

EP - 110

AB - 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.

LA - eng

KW - order-unit space; base-norm space; spectral duality; noncommutative spectral theory of Alfsen and Shultz; norm lower semicontinuous trace

UR - http://eudml.org/doc/215962

ER -

## References

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- [2] E. M. Alfsen, Compact Convex Sets and Boundary Integrals, Ergeb. Math. Grenzgeb. 57, Springer, Berlin 1971. Zbl0209.42601
- [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). Zbl0337.46013
- [4] M. A. Berdikulov, Traces on Jordan algebras, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk 1986 (3), 11-15 (in Russian). Zbl0621.46055
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- [9] D. Petz, Spectral scale of self-adjoint operators and trace inequalities, J. Math. Anal. Appl. 109 (1985), 74-82. Zbl0655.47032
- [10] D. Petz, Jensen's inequality for positive contractions on operator algebras, Proc. Amer. Math. Soc. 99 (1987), 273-277. Zbl0622.46044
- [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). Zbl0719.46035
- [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. Zbl0438.46050

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