Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., R = R = R−1 = ±Im and S = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize ‖AX−Z‖2+‖Y HA−WH‖2, a...

Let n n complex matrices P andQ be nontrivial generalized reflection matrices, i.e., P D P D P 1 ¤ In, Q DQ DQ 1 ¤ In. A complex matrix A with order n is said to be a .P;Q/ generalized anti-reflexive matrix, if PAQ D A. We in this paper mainly investigate the .P;Q/ generalized anti-reflexive maximal and minimal rank solutions to the system of matrix equation AX D B . We present necessary and su...

We give sufficient conditions that allow contractible (resp., reflexive amenable) Banach algebras to be finite-dimensional and semisimple algebras. Moreover, we show that any contractible (resp., reflexive amenable) Banach algebra in which every maximal left ideal has a Banach space complement is indeed a direct sum of finitely many full matrix algebras. Finally, we characterize Hermitian ∗-alg...

We prove that the notions of finite strict singularity, strict singularity and weak compactness coincide for operators defined on various spaces: the disc algebra, subspaces of C(K) with reflexive annihilator and subspaces of the Morse-TransueOrlicz space Mq (Ω, μ) with q > 2.

In this paper, the generalized anti-reflexive solution for matrix equations (BX = C , XD = E), which arise in left and right inverse eigenpairs problem, is considered. With the special properties of generalized anti-reflexive matrices, the necessary and sufficient conditions for the solvability and a general expression of the solution are obtained. Furthermore, the related optimal approximation...

Generalized reflexive solutions of the matrix equation AXB = D and an associated optimal approximation problem a b s t r a c t