Naslov
On projections arising from isometries with finite spectrum on Banach spaces

Autori
Ilišević, Dijana

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
8th Linear Algebra Workshop

Mjesto i datum
Ljubljana, Slovenija, 12.06.2017. - 16.06.2017

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
isometry, spectrum, projection

Sažetak
If P is an orthogonal projection on a Hilbert space, then it can be written in the form P = (I+T)/2 for an isometry (a unitary operator) T satisfying T^2 = I. When looking for a suitable generalization of orthogonal projections in the Banach space setting, the main task is to get rid of the involution in defining an orthogonal projection. One way is to consider Banach space projections that can be written as the average of the identity with an isometric reflection. If T is an isometric reflection then σ(T) = {; ; ; 1, −1}; ; ; , and for P = (I+T)/2 we have T = P − (I − P). More generally, if T is an isometry such that σ(T) = {; ; ; 1, λ}; ; ; with λ \neq 1, then there exists a projection P such that T = P + λ(I − P) ; in this case P is called a generalized bicircular projection. One can also consider generalized n-circular projections that arise from isometries with n distinct eigenvalues. In this talk we shall describe the structure of generalized n-circular projections on some important complex Banach spaces, mostly in the case n=2, but also a few for n \geq 3.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA