Spectral disjointness and invariant subspaces
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences (ICMS 2019)
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Harte, R. (2019). Spectral disjointness and invariant subspaces. International Conference of Mathematical Sciences (ICMS 2019). s. 7.
