| EPSRC Reference: |
GR/S87829/01 |
| Title: |
Operator algebras containing H infinity |
| Principal Investigator: |
Power, Professor S |
| Other Investigators: |
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| Department: |
Mathematics and Statistics |
| Organisation: |
Lancaster University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 May 2004 |
Ends: |
31 August 2004 |
Value (£): |
4,506
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Logic & Combinatorics |
| Mathematical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The modern theory of weakly closed operator algebras addresses algebras that are multiply nonselfadjoint and which are typically generated by families of partial isometries and semigroups of isometries (copies of H infinity ). We intend to study invariant subspaces for a number of such nonselfadjoint operator algebras, notably, (i) translation-multiplication algebras (generalising the Fourier binest algebra), (ii) translation-dilation algebras, (iii) Lie semigroup algebras, and (iv) semigroupoid algebras, including free products and amalgamated free products of H infinity . For the non-free algebras we aim to derive representations of their Hilbert-Schmidt operators and resolve fundamental algebraic questions. These include the nature of ideals and zero divisors as well as synthesis and metric issues of reflexivity and hyper-reflexivity respectively. At the same time we hope to develop a general theory of Lie semigroup algebras going beyond the special cases (i) and (ii). The PI and the proposed fellows David Kribs and Aristides Katavolos have recently developed useful tools and insights for the algebras of (i),(ii),(iv).
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.lancs.ac.uk |