arXiv subjects

Dragan S. Djordjević

Publications and source records attributed to Dragan S. Djordjević.

2 recordsLinked to original sources

arXiv2025

Completion problem of upper triangular $3\times3$ operator matrices on arbitrary Banach spaces

We solve the completion problem of $3\times3$ upper triangular operator matrix acting on a direct sum of Banach spaces and hence generalize the famous result of Han, Lee, Lee (Proc. Amer. Math. Soc. 128 (1) (2000), 119-123) to a greater dimension of a matrix. Our main tools are Harte's ghost of an index theorem and Banach spaces embeddings. We overcome the lack of orthogonality in Banach spaces by exploiting decomposition properties of inner regular operators, and of Fredholm regular operators when needed. Finally, we provide some necessity results related to the invertibility of $n\times n$ upper triangular operators, $n>3$.

math.FA↗

arXiv2014

Group, Moore-Penrose, core and dual core inverse in rings with involution

Let $R$ be a ring with involution. The recently introduced notions of the core and dual core inverse are extended from matrix to an arbitrary $*$-ring case. It is shown that the group, Moore-Penrose, core and dual core inverse are closely related and they can be treated in the same manner using appropriate idempotents. The several characterizations of these inverses are given. Some new properties are obtained and some known results are generalized. A number of characterizations of EP elements in $R$ are obtained. It is shown that core and dual core inverse belong to the class of inverses along an element and to the class of $(b,c)$-inverses. The case when $R$ is algebra of all bounded linear operators on Hilbert space is specifically considered.

math.RA↗