Retraction notice to “Spectral mapping theorem for generalized Kato spectrum” [J. Math. Anal. Appl. 423 (2015) 1–9]

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

The Spectral Mapping Theorem for Joint Approximate Point Spectrum

The spectral mapping theorem for joint approximate point spectrum is proved when A is an «-tuple of commuting operators on a Banach space and ƒ is any w-tuple of rational functions for which f (A) is defined. The purpose of the paper is to show how properties of parts of the joint spectrum can be obtained by use of spaces of sequences of vectors. The method (first used for general Banach spaces...

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Erratum to "Lacunary statistical convergence of multiple sequences" [Appl. Math. Lett. 19(2006) 527-534]

(1) On page 529: The statement “we will denote the set of all double lacunary sequences by Nθr,s ” should be removed. (2) On page 529: In Definition 2.4, the statement “for every ε > 0” should be removed. (3) On page 530: In the proof of (C), for all K should be replaced with for all k and l. (4) The references “Li, J. Lacunary statistical convergence and inclusion properties between lacunary m...