Core theorems for coregular matrices

Localization theorems for eigenvalues of quaternionic matrices

Ostrowski type and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix. We see that the above theorems for the left eigenvalues are also true for the case of right eigenvalues, when the diagonals of quaternionic matrix are real. Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems, respectively, for the ...

Double Sequence Core Theorems

In 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences. Also the core of a double sequence is defined. By using these definitions and the notion of regularity for 4-dimensional matrices, extensions, and variations of the Knopp Core theorem are pro...

Core Equivalence Theorems for Infinite Convex Games

We show that the core of a continuous convex game on a measurable space of players is a von Neumann Morgenstern stable set. We also extend the definition of the Mas Colell bargaining set to games with a measurable space of players and show that for continuous convex games the core may be strictly included in the bargaining set but it coincides with the set of all countably additive payoff measu...

Theorems and counterexamples on structured matrices

Comparison theorems using general cones for norms of iteration matrices

We prove comparison theorems for norms of iteration matrices in splittings of matrices in the setting of proper cones in a finite dimensional real space by considering cone linear absolute norms and cone max norms. Subject to mild additional hypotheses, we show that these comparison theorems can hold only for such norms within the class of cone absolute norms. Finally, in a Banach algebra setti...