SavedAdd your journal

Journals / 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
Pages
—
Publication Date
2025-08-29
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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 Key Takeaways

🎯
Objective & Hypothesis:We extend several notions such as semi-continuity and Jensen measures for matrix-valued functions.
📊
Key Findings & Data:For that purpose, we introduce $\Gamma$-order on noncommutative matrix spaces.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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.

🔖

Cite This Article

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

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. C. D. Aliprantis and O. Burkinshaw, Positive Operators, Springer, 2006.
  2. R. R. Coifman and S. Semmes, Interpolation of Banach Spaces, Perron Processes, and Yang-Mills, Am. J. Math. 115 (2), 243278, 1993.
  3. J. B. Conway, A course in Functional Analysis, Springer, 1997.
  4. N. Dinculeanu, Vector Measures, Pergamon Press, 1967.
  5. D.A. Edwards, Choquet boundary theory for certain spaces of lower semicontinuous functions, in Function Algebras (Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965 (Birtel, F., ed.)), 300-309, Scott-Foresman, Chicago, Ill., 1966.
  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.