Reverse order laws in C∗-algebras

Reverse order law in C∗-algebras

We study equivalent conditions for the reverse order law (a1a2 . . . an)† = an(a † 1a1a2 . . . ana † n) †a1 in C ∗-algebras. As corollaries, we obtain some recent and special results.

Reverse order laws for {1, 3, 4}-generalized inverses in C*-algebras

In this paper, we consider the reverse order laws for {1, 3, 4}-generalized inverses in C*algebras. We present purely algebraic necessary and sufficient conditions for b{1, 3, 4}· a{1, 3, 4} ⊆ (ab){1, 3, 4} and (ab){1, 3, 4} = b{1, 3, 4} · a{1, 3, 4}. Also, we prove that (ab){1, 3, 4} ⊆ b{1, 3, 4} · a{1, 3, 4} is actually equivalent to (ab){1, 3, 4} = b{1, 3, 4} · a{1, 3, 4}. 2010 Mathematics S...

The reverse order laws and the mixed-type reverse order laws for generalized inverses of multiple matrix products

Ela the Reverse Order Laws and the Mixed-type Reverse Order Laws for Generalized Inverses of Multiple Matrix Products

In this paper, necessary and sufficient conditions for a number of reverse order laws and mixed-type reverse order laws are derived by using the maximal ranks of the generalized Schur complements.

Ela Reverse Order Law for the Moore-penrose Inverse in C∗-algebras∗

In this paper, several equivalent conditions related to the reverse order law for the Moore-Penrose inverse in C-algebras are studied. Some well-known results are extended to more general settings. Then this result is applied to obtain the reverse order rule for the weighted Moore-Penrose inverse in C-algebras.