Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extension of Finite Rank Operators and Local Structures in Operator
  Ideals   We develop general techniques and present an approach to solve the problem of
constructing a maximal Banach ideal $({\frak A},{\bf A)}$ which does not
satisfy a transfer of the norm estimation in the principle of local reflexivity
to its norm ${\bf A}$. This approach leads us to the investigation of product
operator ideals containing ${\frak L}_2$ (the collection of all Hilbertian
operators) as a factor. Using the local properties of such operator ideals --
which are typical examples of ideals with property (I) and property (S) --,
trace duality and an extension of suitable finite rank operators even enable us
to show that ${\frak L}_\infty $ cannot be totally accessible -- answering an
open question of Defant and Floret.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys