Bull. Austral. Math. Soc. 72(3) pp.407--421, 2005.

Similarity invariant semigroups generated by
non-Fredholm operators

Iztok Kavkler

Received: 5th July, 2005

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Abstract

Let A $ \in $ B($ \hs $) be a bounded non-compact operator that is not semi-Fredholm. The similarity invariant semigroup generated by A is shown to consist of all operators that are not semi-Fredholm and satisfy obvious inequalities for the nullity and co-nullity.

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(Metadata: XML, RSS, BibTeX) MathSciNet: MR2199643 Z'blatt-MATH: 1103.47029

References

  1. A. Brown and C. Pearcy;
    Structure of commutators of operators,
    Ann. of Math. (2) 82 (1965), pp. 112--127. MR178354
  2. R.J.H. Dawlings;
    The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space,
    Proc. Roy. Soc. Edinburgh 94 (1983), pp. 351--360. MR709728
  3. R.G. Douglas;
    On majorization, factorization, and range inclusion of operators on {H}ilbert space,
    Proc. Amer. Math. Soc. 17 (1966), pp. 413--415. MR203464
  4. P.A. Fillmore, J.G. Stampfli, and J.P. Williams;
    On the essential numerical range, the essential spectrum, and a problem of {H}almos,
    Acta Sci. Math. (Szeged) 33 (1972), pp. 179--192. MR322534
  5. P.A. Fillmore and J.P. Williams;
    On operator ranges,
    Advances in Math. 7 (1971), pp. 254--281. MR293441
  6. C.K. Fong and A.R. Sourour;
    The semigroup generated by a similarity orbit or a unitary orbit of an operator,
    Proc. Amer. Math. Soc. 131 (2003), pp. 3203--3210. MR1992861
  7. I. Kavkler;
    Semigroups generated by similarity orbits of semi-invertible operators and unitary orbits of isometries,
    Semigroup Forum 68 (2004), pp. 293--303. MR2036629
  8. N.C. Phillips;
    Every invertible {H}ilbert space operator is a product of seven positive operators,
    Canad. Math. Bull. 38 (1995), pp. 230--236. MR1335103

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