Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extreme contractions on finite-dimensional polygonal Banach spaces   We explore extreme contractions between finite-dimensional polygonal Banach
spaces, from the point of view of attainment of norm of a linear operator. We
prove that if $ X $ is an $ n- $dimensional polygonal Banach space and $ Y $ is
any Banach space and $ T \in L(X,Y) $ is an extreme contraction, then $ T $
attains norm at $ n $ linearly independent extreme points of $ B_{X}. $
Moreover, if $ T $ attains norm at $ n $ linearly independent extreme points $
x_1, x_2, \ldots, x_n $ of $ B_X $ and does not attain norm at any other
extreme point of $ B_X, $ then each $ Tx_i $ is an extreme point of $ B_Y.$ We
completely characterize extreme contractions between a finite-dimensional
polygonal Banach space and a strictly convex Banach space. We introduce L-P
property for a pair of Banach spaces and show that it has natural connections
with our present study. We also prove that for any strictly convex Banach space
$ X $ and any finite-dimensional polygonal Banach space $ Y, $ the pair $ (X,Y)
$ does not have L-P property. Finally, we obtain a characterization of Hilbert
spaces among strictly convex Banach spaces in terms of L-P property.

23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga