The paper provides extensive and systematic investigations of k-potent complex matrices, with a particular attention paid to tripotent matrices. Several new properties of k-potent matrices are identified. Furthermore, some results known in the literature are reestablished with simpler proofs than in the original sources and often in a generalized form.

In this note we give an index theory for Toeplitz operators on the Hardy space of the Shilov boundary of an arbitrary bounded symmetric domain. Our results generalize earlier work of Gohberg-Krein and Venugopalkrishna [12] for domains of rank 1 and of Berger-Coburn-Koranyi [1] for domains of rank 2. Bounded symmetric domains (Cartan domains, classical or exceptional) are the natural higher-dime...

We study the spectrum and the rank of a linear combination of two orthogonal projectors. We characterize when this linear combination is EP, diagonalizable, idempotent, tripotent, involutive, nilpotent, generalized projector, and hypergeneralized projector. Also we derive the Moore-Penrose inverse of a linear combination of two orthogonal projectors in a particular case. The main tool used here...

BACKGROUND Despite the suitability of a mouse model for preclinical investigations; little is known regarding mesenchymal stem cells derived from murine amniotic fluid. This is the subject of the present study.  METHODS   Amniotic fluid was collected from NMRI mice during the second weeks of pregnancy and plated. The cells that adhered to the culture surfaces were propagated with three succes...

A new class of rings are introduced which every element in the ring sum involution and tripotent elements. This called t-clean is a generalization invo-clean subclass clean rings. Some properties this investigate. For an application graph theory, defined set vertices order pairs them element. The two adjacent if only elements zero or product zero. graphs connecting, has diameter one girth three.

Bounded symmetric domains (Cartan domains and exceptional domains) are higher-dimensional generalizations of the open unit disc. In this note we give a structure theory for the C*-algebra T generated by all Toeplitz operators Tf(h) := P{fh) with continuous symbol function ƒ G C(S) on the Shilov boundary 5 of a bounded symmetric domain D of arbitrary rank r. Here h belongs to the Hardy space H(S...