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Seddighin, Morteza

Approximations of antieigenvalue and antieigenvalue-type quantities. (English) Zbl 1279.47054

Int. J. Math. Math. Sci. 2012, Article ID 318214, 15 p. (2012).
The author extends the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type inequalities are analogous to those of antieigenvalue and Kantorovich inequality. In the second section, the author approximates several antieigenvalue-type quantities for arbitrary accretive operators. Each antieigenvalue-type quantity is approximated in terms of the same quantity for normal matrices. In particular, the author shows that, for an arbitrary accretive operator, each antieigenvalue-type quantity is the limit of the same quantity for a sequence of finite-dimensional normal matrices.
Reviewer: Bilender P. Allahverdiev (Isparta)

Cited in 1 Document

MSC:

47B44 Linear accretive operators, dissipative operators, etc.
47A10 Spectrum, resolvent
47A75 Eigenvalue problems for linear operators

Keywords:

accretive operators; antieigenvalue; antieigenvalue-type quantities; Kantorovich-type inequalities
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\textit{M. Seddighin}, Int. J. Math. Math. Sci. 2012, Article ID 318214, 15 p. (2012; Zbl 1279.47054)
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