• Title/Summary/Keyword: Schur product theorem

Search Result 2, Processing Time 0.014 seconds

C*-ALGEBRAIC SCHUR PRODUCT THEOREM, PÓLYA-SZEGŐ-RUDIN QUESTION AND NOVAK'S CONJECTURE

  • Krishna, Krishnanagara Mahesh
    • Journal of the Korean Mathematical Society
    • /
    • v.59 no.4
    • /
    • pp.789-804
    • /
    • 2022
  • Striking result of Vybíral [51] says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vybíral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C*-algebras and derive the results of Schur and Vybíral. As an application, we state C*-algebraic version of Novak's conjecture and solve it for commutative unital C*-algebras. We formulate Pólya-Szegő-Rudin question for the C*-algebraic Schur product of positive matrices.

SCHATTEN'S THEOREM ON ABSOLUTE SCHUR ALGEBRAS

  • Rakbud, Jitti;Chaisuriya, Pachara
    • Journal of the Korean Mathematical Society
    • /
    • v.45 no.2
    • /
    • pp.313-329
    • /
    • 2008
  • In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten's Theorem on the Banach space $B(l_2)$ of bounded linear operators on $l_2$ involving the duality relation among the class of compact operators K, the trace class $C_1$ and $B(l_2)$. We also study the reflexivity in such the algebras.