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**The Browder spectrum of an elementary operator.** / Kitson, Derek.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed)

Kitson, D 2011, The Browder spectrum of an elementary operator. in R Curto & M Mathieu (eds), *Elementary operators and their applications : 3rd International Workshop held at Queen's University Belfast, 14-17 April 2009.* Operator Theory: Advances and Applications, vol. 212, Birkhäuser Verlag, Basel, pp. 17-24. https://doi.org/10.1007/978-3-0348-0037-2_2

Kitson, D. (2011). The Browder spectrum of an elementary operator. In R. Curto, & M. Mathieu (Eds.), *Elementary operators and their applications : 3rd International Workshop held at Queen's University Belfast, 14-17 April 2009 *(pp. 17-24). (Operator Theory: Advances and Applications; Vol. 212). Birkhäuser Verlag. https://doi.org/10.1007/978-3-0348-0037-2_2

Kitson D. The Browder spectrum of an elementary operator. In Curto R, Mathieu M, editors, Elementary operators and their applications : 3rd International Workshop held at Queen's University Belfast, 14-17 April 2009. Basel: Birkhäuser Verlag. 2011. p. 17-24. (Operator Theory: Advances and Applications). https://doi.org/10.1007/978-3-0348-0037-2_2

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title = "The Browder spectrum of an elementary operator",

abstract = "We relate the ascent and descent of n-tuples of multiplication operators Ma,b(u)=aub to that of the coefficient Hilbert space operators a, b. For example, if a=(a1,…,an) and b∗=(b∗1,…,b∗m) have finite non-zero ascent and descent s and t, respectively, then the (n+m) -tuple (La,Rb) of left and right multiplication operators has finite ascent and descent s+t−1. . Using these results we obtain a description of the Browder joint spectrum of (La,Rb) and provide formulae for the Browder spectrum of an elementary operator acting on B(H) or on a norm ideal of B(H).",

author = "Derek Kitson",

year = "2011",

doi = "10.1007/978-3-0348-0037-2_2",

language = "English",

isbn = "9783034800365",

series = "Operator Theory: Advances and Applications",

publisher = "Birkh{\"a}user Verlag",

pages = "17--24",

editor = "Raul Curto and Martin Mathieu",

booktitle = "Elementary operators and their applications",

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T1 - The Browder spectrum of an elementary operator

AU - Kitson, Derek

PY - 2011

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N2 - We relate the ascent and descent of n-tuples of multiplication operators Ma,b(u)=aub to that of the coefficient Hilbert space operators a, b. For example, if a=(a1,…,an) and b∗=(b∗1,…,b∗m) have finite non-zero ascent and descent s and t, respectively, then the (n+m) -tuple (La,Rb) of left and right multiplication operators has finite ascent and descent s+t−1. . Using these results we obtain a description of the Browder joint spectrum of (La,Rb) and provide formulae for the Browder spectrum of an elementary operator acting on B(H) or on a norm ideal of B(H).

AB - We relate the ascent and descent of n-tuples of multiplication operators Ma,b(u)=aub to that of the coefficient Hilbert space operators a, b. For example, if a=(a1,…,an) and b∗=(b∗1,…,b∗m) have finite non-zero ascent and descent s and t, respectively, then the (n+m) -tuple (La,Rb) of left and right multiplication operators has finite ascent and descent s+t−1. . Using these results we obtain a description of the Browder joint spectrum of (La,Rb) and provide formulae for the Browder spectrum of an elementary operator acting on B(H) or on a norm ideal of B(H).

U2 - 10.1007/978-3-0348-0037-2_2

DO - 10.1007/978-3-0348-0037-2_2

M3 - Chapter (peer-reviewed)

SN - 9783034800365

T3 - Operator Theory: Advances and Applications

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BT - Elementary operators and their applications

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A2 - Mathieu, Martin

PB - Birkhäuser Verlag

CY - Basel

ER -