Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: F\olner sequences and finite operators   This article analyzes F\olner sequences of projections for bounded linear
operators and their relationship to the class of finite operators introduced by
Williams in the 70ies. We prove that each essentially hyponormal operator has a
proper F\olner sequence (i.e. a F\olner sequence of projections strongly
converging to 1). In particular, any quasinormal, any subnormal, any hyponormal
and any essentially normal operator has a proper F\olner sequence. Moreover, we
show that an operator is finite if and only if it has a proper F\olner sequence
or if it has a non-trivial finite dimensional reducing subspace. We also
analyze the structure of operators which have no F\olner sequence and give
examples of them. For this analysis we introduce the notion of strongly
non-F\olner operators, which are far from finite block reducible operators, in
some uniform sense, and show that this class coincides with the class of
non-finite operators.

22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ