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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 4

Edwards' Theorem and matrix-valued functions

Umutcan Erdur(SABANCI UNIVERSITY)0000-0003-4608-4572
Nihat Gökhan Göğüş(SABANCI UNIVERSITY)0000-0003-1966-8409
Sayfa
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Yayın Tarihi
2025-08-29
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Afterward, we generalize the Edwards' Theorem for a noncommutative matrix space by exploiting properties of $\Gamma$-order given on the matrix space which we consider.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We extend several notions such as semi-continuity and Jensen measures for matrix-valued functions.
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Temel Bulgular & Veri:For that purpose, we introduce $\Gamma$-order on noncommutative matrix spaces.
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Sonuç & Katkı:Afterward, we generalize the Edwards' Theorem for a noncommutative matrix space by exploiting properties of $\Gamma$-order given on the matrix space which we consider.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:matrix-valued functions · Jensen measures · Edwards’ Theorem

Abstract

We extend several notions such as semi-continuity and Jensen measures for matrix-valued functions. For that purpose, we introduce $\Gamma$-order on noncommutative matrix spaces. Afterward, we generalize the Edwards' Theorem for a noncommutative matrix space by exploiting properties of $\Gamma$-order given on the matrix space which we consider.

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Bu Makaleye Atıf Yap

Erdur, U., Göğüş, N. G. (2025). Edwards' Theorem and matrix-valued functions. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 4. https://doi.org/10.15672/hujms.1478167

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Kaynakça (11)

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  6. T.W. Gamelin, Uniform Algebras and Jensen Measures, London Mathematical Society Lecture Notes Series 32, Cambridge University Press, Cambridge, 1978.
  7. L. Lempert, Noncommutative Potential Theory, Analysis Math. 28 (4), 603-627, 2017.
  8. M. P. Olson, The selfadjoint operators of a Von Neumann algebra form a conditionally complete lattice, Proc. Amer. Soc. 28, 537-544, 1971.
  9. W. Rudin, Functional Analysis, McGraw-Hill Book Company, New York, 1973.
  10. S. Sherman, Order in Operator Algebras, Am. J. Math. 73 (1), 22732, 1951.
  11. F. Wikström, Jensen Measures and boundary values of plurisubharmonic functions, Ark. Mat. 39, 181-200, 2001.