Spectral disjointness and invariant subspaces
| dc.contributor.author | Harte, Robin | |
| dc.date.accessioned | 2024-07-12T20:49:20Z | |
| dc.date.available | 2024-07-12T20:49:20Z | |
| dc.date.issued | 2019 | en_US |
| dc.department | Fakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümü | en_US |
| dc.description.abstract | Spectral disjointness confers a certain ”independence” upon linear operators. If G is a ring with identity I then an idempotent Q = Q2 ? G gives the ring G a block structure G ?= A M N B where for example A = QGQ; then T = a m n b ? G commutes with Q iff it is a ”block diagonal”: T Q = QT ?? T = a 0 0 b . Specialising to complex Banach algebras, for block diagonals there is two way implication ?A(a) ? ?B(b) = ? ?? Q ? Holo(T) : Q = f(T) with f : U ? G holomorphic on an open neighbourhood of ?G(T). Weaker spectral disjointness gives a little less: ? lef t A (a) ? ? right B (b) = ? =? Q ? comm2 (T) : the block structure idempotent Q “double commutes” with T ? G. Specializing to G = B(X), the bounded operators on a Banach space, closed complemented subspaces Y ? X give us again the block structure, and operators T ? G for which Y is “invariant” become “block triangles”: T(Y ) ? Y ?? T = a m 0 b . When Y ? X is not complemented then the block structure is missing and we must resort to the restriction and the quotient: a = TY ? A = B(Y ) ; b = T/Y ? B(X/Y ) . Now spectral disjointness ?A(a) ? ?B(b) = ? ensures that the subspace Y ? X is both hyperinvariant and reducing, in particular complemented. | en_US |
| dc.identifier.citation | Harte, R. (2019). Spectral disjointness and invariant subspaces. International Conference of Mathematical Sciences (ICMS 2019). s. 7. | en_US |
| dc.identifier.endpage | 7 | en_US |
| dc.identifier.isbn | 978-605-2124-29-1 | |
| dc.identifier.startpage | 7 | en_US |
| dc.identifier.uri | https://hdl.handle.net/20.500.12415/2159 | |
| dc.institutionauthor | Harte, Robin | |
| dc.language.iso | en | en_US |
| dc.publisher | Maltepe Üniversitesi | en_US |
| dc.relation.ispartof | International Conference of Mathematical Sciences (ICMS 2019) | en_US |
| dc.relation.publicationcategory | Uluslararası Konferans Öğesi - Başka Kurum Yazarı | en_US |
| dc.rights | CC0 1.0 Universal | * |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.rights.uri | http://creativecommons.org/publicdomain/zero/1.0/ | * |
| dc.snmz | KY01524 | |
| dc.title | Spectral disjointness and invariant subspaces | en_US |
| dc.type | Article | |
| dspace.entity.type | Publication |
