A selfadjoint involutive matrix J endows Cn with an indefinite inner product [·,·] given by [x,
y]=〈 Jx, y〉, x, y∈ Cn. Characterizations of the J-chaotic order Log (A)⩾ J Log (B) are …

For a selfadjoint involutive matrix J we equip C n with the indefinite inner product [x, y]=< J x,
y>, where<⋅,⋅> denotes the usual inner product on C n and endow the matrix algebra M n …

Let J be a non trivial involutive Hermitian matrix. Consider C n equipped with the indefinite
inner product induced by J,[x, y]= y∗ J x for all x, y∈ C n, which endows the matrix algebra C …

In this paper, the arithmetic-geometric mean inequalities of indefinite type are discussed. We
show that for a J-selfadjoint matrix A satisfying I≥ JA and sp (A)⊆[1,∞), the inequality I+ A …

In the set up of Minkowski spaces, the Schwarz inequality holds with the reverse inequality
sign. As a consequence, the same occurs with the triangle inequality. In this note, extensions …

In 1987, we established an operator inequality as follows; $ A\ge B\ge 0$$\Longrightarrow
(A^{\frac {r}{2}} A^ p A^{\frac {r}{2}})^{\frac {1}{q}}\ge (A^{\frac {r}{2}} B^ p A^{\frac {r}{2}})^{\frac …

A selfadjoint involutive matrix J endows Cn with an indefinite inner product [·,·] given by [x,
y]:=〈 J x, y〉, x, y∈ Cn. We present some inequalities of indefinite type involving the α …

Several inequalities have been established in the context of Hilbert spaces operators or
operator algebras. Our discussion will be limited to matrices. Important inequalities in …

A FIEDLER–TYPE THEOREM FOR THE DETERMINANT OF J–POSITIVE MATRICES 1.
Introduction Let A and C be Hermitian n×n matrices wit Page 1 M athematical I nequalities & A …

Spectral inequalities are stated for the trace of the exponential or the logarithmic of certain J-
Hermitian matrices, J= Ir⊕-In-r, 0< r< n. The obtained inequalities are established in the …