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Powers of Rdiagonal Elements
 Journ. Operator Theory
, 1999
"... We prove that if (a; b) is an Rdiagonal pair in some noncommutative probability space (A; ') then (a p ; b p ) is Rdiagonal too and we compute the determining series f (a p ;b p ) in terms of the distribution of ab. We give estimates of the upper and lower bounds of the support of f ..."
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Cited by 12 (0 self)
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of free multiplicative convolution of probability measures compactly supported on [0; 1[, and use the results to give norm estimates of powers of Rdiagonal elements in finite von Neumann algebras. Finally we compute norms, distributions and Rtransforms related to powers of the circular element. 1
Strong Haagerup inequalities for free Rdiagonal elements
 J. FUNCT. ANAL
, 2007
"... In this paper, we generalize Haagerup’s inequality [H] (on convolution norm in the free group) to a very general context of Rdiagonal elements in a tracial von Neumann algebra; moreover, we show that in this “holomorphic” setting, the inequality is greatly improved from its originial form. We give ..."
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Cited by 15 (6 self)
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In this paper, we generalize Haagerup’s inequality [H] (on convolution norm in the free group) to a very general context of Rdiagonal elements in a tracial von Neumann algebra; moreover, we show that in this “holomorphic” setting, the inequality is greatly improved from its originial form. We
On constructing matrices with prescribed singular values and diagonal elements
, 1998
"... Abstract. Similar to the well known SchurHorn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix, the SingThompson theorem characterizes the relationship between the diagonal entries and the singular values of an arbitrary matrix. It ..."
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Cited by 6 (5 self)
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. It is noted in this paper that, based on the induction principle, such a matrix can be constructed numerically by a fast recursive algorithm, provided that the given singular values and diagonal elements satisfy the SingThompson conditions. 1. Introduction. It
Relations between the diagonal elements of two mutually inverse positive definite matrices
 Czechoslovak Math. J
, 1964
"... Relations between the diagonal elements of two mutually inverse positive definite matrices ..."
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Cited by 4 (1 self)
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Relations between the diagonal elements of two mutually inverse positive definite matrices
Maximality of the microstates free entropy for Rdiagonal elements
 the Pacific Journal of Mathematics
"... A noncommutative nonself adjoint random variable z is called Rdiagonal, if its ∗distribution is invariant under multiplication by free unitaries: if a unitary w is ∗free from z, then the ∗distribution of z is the same as that of wz. Using Voiculescu’s microstates definition of free entropy, we ..."
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Cited by 12 (3 self)
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, we show that the Rdiagonal elements are characterized as having the largest free entropy among all variables y with a fixed distribution of y ∗ y. More generally, let Z be a d×d matrix whose entries are noncommutative random variables Xij, 1≤i, j ≤ d. Then the free entropy of the family {Xij
A NOTE ON ESTIMATES OF DIAGONAL ELEMENTS OF THE INVERSE OF DIAGONALLY DOMINANT TRIDIAGONAL MATRICES
, 2008
"... ABSTRACT. In this note we show how to improve some recent upper and lower bounds for the elements of the inverse of diagonally dominant tridiagonal matrices. In particular, a technique described by [R. Peluso, and T. Politi, Some improvements on twosided bounds on the inverse of diagonally dominant ..."
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ABSTRACT. In this note we show how to improve some recent upper and lower bounds for the elements of the inverse of diagonally dominant tridiagonal matrices. In particular, a technique described by [R. Peluso, and T. Politi, Some improvements on twosided bounds on the inverse of diagonally
A TradeOff for Covering the OffDiagonal Elements of Matrices
"... We would like to cover all the offdiagonal elements of an n\Thetan matrix by nonnecessarily contiguous rectangular submatrices; the diagonal elements cannot be covered. It is not difficult to give a cover with 2dlog ne rectangles, where some offdiagonal elements are covered as many as dlog netim ..."
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We would like to cover all the offdiagonal elements of an n\Thetan matrix by nonnecessarily contiguous rectangular submatrices; the diagonal elements cannot be covered. It is not difficult to give a cover with 2dlog ne rectangles, where some offdiagonal elements are covered as many as dlog ne
Invariants of Triangular Lie Algebras with One Nilindependent Diagonal Element
, 705
"... The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan’s method of moving frames and the special technique developed f ..."
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Cited by 1 (1 self)
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The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan’s method of moving frames and the special technique developed
c Copyright by Theta, 2002 POWERS OF RDIAGONAL ELEMENTS
"... Abstract. We prove that if (a; b) is an Rdiagonal pair in some noncommutative probability space (A;') then (ap; bp) is Rdiagonal too and we compute the determining series f(ap;bp) in terms of the distribution of ab. We give estimates of the upper and lower bounds of the support of free mult ..."
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multiplicative convolution of probability measures compactly supported on [0;1[, and use the results to give norm estimates of powers of Rdiagonal elements in nite von Neumann algebras. Finally we compute norms, distributions and Rtransforms related to powers of the circular element.
Results 1  10
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363,155