Interaction antieigenvalues

Abstract

The notion of interaction antieigenvalue, which I mentioned over thirty years ago but which to date has not been elaborated, will be briefly elaborated here. New bounds will be obtained from it.

The Trigonometry of Matrix Statistics

“…I have used the function f ºt» º½ t» º½ t» several times in the matrix trigonometry. An interesting recent application not totally unlike the one just given above may be found in Gustafson (2004), see the bottom of p. 178 there.…”

On the joint antieigenvalues of operators in normal subalgebras

“…The GreubRheinboldt inequality is one of a set of "complementary inequalities" and we refer to the recent paper Gustafson [6] for further background and literature citations. In [6] the GreubRheinboldt inequality is treated for two commuting selfadjoint operators.…”

“…The GreubRheinboldt inequality is one of a set of "complementary inequalities" and we refer to the recent paper Gustafson [6] for further background and literature citations. In [6] the GreubRheinboldt inequality is treated for two commuting selfadjoint operators. To connect to the treatment of [6] with that of the present paper, we note that if A(H ) is a commutative closed subalgebra of B(H ) whose elements are SPD operators, then its elements can be written in terms of the same spectral family.…”

“…In [6] the GreubRheinboldt inequality is treated for two commuting selfadjoint operators. To connect to the treatment of [6] with that of the present paper, we note that if A(H ) is a commutative closed subalgebra of B(H ) whose elements are SPD operators, then its elements can be written in terms of the same spectral family. Assume T and S are two elements of A(H ) with eigenvalues {β i } ∞ i=1 and {α i } ∞ i=1 , respectively, then the expression (20) will be reduced to 2 √ α i α j β i β j α i α j +β i β j .…”

“…In [6] Gustafson has also generalized Greub-Rheinboldt inequality to two SPD operators which may not commute.…”