- Titolo:
- Spectral flows on Banach spaces and disconnected conjugacy classes of projectors in direct sums of sequences spaces
- Quando:
- 27.01.2017 11.30 h
- Dove:
- Palazzo Campana - Torino
- Aula:
- Aula C
- Relatore:
- Dott. Daniele Garrisi
- Afferenza:
- Inha University, South Corea
- Proponente:
- V. Barutello
- Locandina:

Some definitions of spectral flow require a subdivision of the interval of definition into subintervals, where it is possible to define continuously paths of spectral projections. This method has been used by J. Phillips (1996), with the intention of providing a definition of spectral flow for continuous paths without using smooth paths as intermediate step. In this presentation we show that this definition can be simplified further if just one refrains from requiring the projections to be spectral. This simplification allows us to characterize the kernel and the image of the spectral flow in Banach spaces, and exhibit examples of spaces, where the spectral flow is not a group isomorphism, unlike infinite-dimensional Hilbert spaces. This difference amounts to the following behavior:

(1) the existence of infinite-dimensional spaces which are not isomorphic to closed subspaces of finite co-dimension

(2) the existence of pairs of projectors which are conjugated to each other, but there is no continuous path of projectors connecting one to the other.

We will focus on examples of projectors as in (2) arising in Banach spaces which can be obtained as a finite direct sums of sequences spaces \(\mathcal{l}_p \).

- Sede:
- Palazzo Campana - Sito web
- Via:
- Via Carlo Alberto, 10
- Cap:
- 10123
- CittÃ :
- Torino
- Provincia:
- To
- Paese:

Dipartimento di Matematica, UniversitÃ degli Studi di Torino