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    Pseudospectrum of an element of a Banach algebra (Pre-published version)

    Citation

    Kulkarni, S. H. and Krishnan, A. (2017) 'Pseudospectrum of an element of a Banach algebra', Operators and Matrices, 11(1), 263-287, available: https://doi.org/10.7153/oam-11-18.
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    Kulkarni, S. H. and Krishnan, A. (2017) Pseudospectrum of an element of a Banach algebra.pdf (242.9Kb)
    Date
    2017-03
    Author
    Kulkarni, S H
    Krishnan, Arundhathi
    Peer Reviewed
    Yes
    Metadata
    Show full item record
    Kulkarni, S. H. and Krishnan, A. (2017) 'Pseudospectrum of an element of a Banach algebra', Operators and Matrices, 11(1), 263-287, available: https://doi.org/10.7153/oam-11-18.
    Abstract
    The ε -pseudospectrum Λε (a) of an element a of an arbitrary Banach algebra A is studied. Its relationships with the spectrum and numerical range of a are given. Characterizations of scalar, Hermitian and Hermitian idempotent elements by means of their pseudospectra are given. The stability of the pseudospectrum is discussed. It is shown that the pseudospectrum has no isolated points, and has a finite number of components, each containing an element of the spectrum of a. Suppose for some ε > 0 and a,b ∈ A, Λε (ax) = Λε(bx) ∀x ∈ A. It is shown that a = b if: (i) a is invertible. (ii) a is Hermitian idempotent. (iii) a is the product of a Hermitian idempotent and an invertible element. (iv) A is semisimple and a is the product of an idempotent and an invertible element. (v) A = B(X) for a Banach space X . (vi) A is a C∗-algebra. (vii) A is a commutative semisimple Banach algebra.
    Keywords
    Banach algebra
    Hermitian
    Idempotent
    Numerical range
    Pseudospectrum
    Semisimple
    Spectrum
    Language (ISO 639-3)
    eng
    Publisher
    Element Publishing House
    Rights
    Open Access
    License URI
    https://oam.ele-math.com/
    DOI
    10.7153/oam-11-18
    URI
    https://dspace.mic.ul.ie/handle/10395/3336
    ISSN
    1848-9974
    Collections
    • Mathematics and Computer Studies (Peer-reviewed publications)

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