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1.
Another note on Weyl's theorem   总被引:24,自引:0,他引:24  
``Weyl's theorem holds" for an operator on a Banach space when the complement in the spectrum of the ``Weyl spectrum" coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity. This is close to, but not quite the same as, equality between the Weyl spectrum and the ``Browder spectrum", which in turn ought to, but does not, guarantee the spectral mapping theorem for the Weyl spectrum of polynomials in . In this note we try to explore these distinctions.

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2.
Reverse order laws in C-algebras   总被引:1,自引:0,他引:1  
In this paper, we offer purely algebraic necessary and sufficient conditions for reverse order laws for generalized inverses in C-algebras, extending rank conditions for matrices and range conditions for Hilbert space operators.  相似文献
3.
A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.

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4.
The spectral pictures of products and of Banach space operators are compared; in particular when one of them is `of index zero'.

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5.
``Polaroid elements" represent an attempt to abstract part of the condition, ``Weyl's theorem holds" for operators.

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6.
We offer a perturbation theory for finite ascent and descent properties of bounded operators.

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7.

``Reduction" of linear operators is effected by commuting projections; the spectrum of the operator is then the union of the spectra of its range and null space restrictions. Disjointness of these partial spectra implies that the projection ``double commutes" with the operator, which in turn can be recognised as a curious kind of ``exactness". Variants of this exactness correspond to various kinds of disjointness between the partial spectra.

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8.

The ``ghost of an index theorem" is an isomorphism between products of the kernel spaces and the cokernel spaces of a pair of bounded operators and their product, valid when each operator and also the product is assumed to have a generalized inverse. In this note we correct an error in the original proof, and extend the result to operators with closed range.

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9.
The Taylor spectrum of a mixed pair of multiplication operators is determined on an ultraprime Banach algebra.

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10.
The ``bounded closure of the range" of an operator between two normed spaces is a linear subspace lying between the range and its closure. The induced concept of ``almost onto" is a sort of first draft of the concept of ``almost open".

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