Positive Definite Functions and Operator Inequalities

By Rajendra Bhatia, K. Parthasarathy. 2000

85 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6f6e5803950deabf4cca2c98fa600f5cebeaf8e7

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Young-type inequalities and their matrix analogues (2015, unknown): “The Frobenius norm version of Young’s inequality was established by Kosaki [15] and in case A = B also by Bhatia and Parthasarathy [16] as ‖Aν X B1−ν‖2 ≤ ‖ν AX + (1 − ν)X B‖2, (5.”
Reverse Young and Heinz inequalities for matrices (2011, background): “which is an improvement of the matrix Young inequality for the Hilbert–Schmidt norm [2] and [7].”
The matrix arithmetic-geometric mean inequality revisited (2008, background): “In [15,31] the authors establish a connection between such matrices and the theory of positive definite functions.”
Cauchy–Schwarz norm inequalities for weak∗-integrals of operator valued functions (2005, background): “Hadamard product and positive definite functions play also an important role in those inequalities for finite matrices, greatly contributing to their more systematic understanding (see [10]).”
On the exponential metric increasing property (2003, methodology): “This is true [5,9], though harder to prove.”
Interpolating the arithmetic-geometric mean inequality and its operator version (2006, methodology): “This technique turned out to be very useful and was applied to many examples in [4].”
Infinitely Divisible Matrices (2006, background): “It is known [5] that for each t in (2, ∞) there exists an n for which the n × n matrix Z is not positive semidefinite for some choice of numbers λ1, .”
Matrix Young inequalities for the Hilbert–Schmidt norm (2000, background): “Kosaki [12] and Bhatia and Parthasarathy [6] pointed out that ifA,B,X ∈ Mn(C) such thatA andB are positive semidefinite and if p, q > 1 with 1 p + 1 q = 1, then ∥∥∥ 1 pApX + 1 q XB ∥∥∥ 2 > ‖AXB‖2 .”