TY - JOUR
T1 - Three kinds of numerical indices of a Banach space II
AU - Kim, Sung Guen
N1 - Publisher Copyright:
© 2016 NISC (Pty) Ltd.
PY - 2016/3/31
Y1 - 2016/3/31
N2 - For a Banach space E and a positive integer k, we study about three kinds of numerical indices of E, the multilinear numerical index (Formula presented.) (E), the symmetric multilinear numerical index (Formula presented.) (E) and the polynomial numerical index (Formula presented.) (E). First we show that (Formula presented.) (E**) ≤ (Formula presented.) (E) for I=m, s and present some inequalities among (Formula presented.) (E), (Formula presented.) (E) and (Formula presented.) (E). We also prove that if E is a strictly convex Banach space, then (Formula presented.) (E)=0 for every k ≥ 2.
AB - For a Banach space E and a positive integer k, we study about three kinds of numerical indices of E, the multilinear numerical index (Formula presented.) (E), the symmetric multilinear numerical index (Formula presented.) (E) and the polynomial numerical index (Formula presented.) (E). First we show that (Formula presented.) (E**) ≤ (Formula presented.) (E) for I=m, s and present some inequalities among (Formula presented.) (E), (Formula presented.) (E) and (Formula presented.) (E). We also prove that if E is a strictly convex Banach space, then (Formula presented.) (E)=0 for every k ≥ 2.
KW - homogeneous polynomials
KW - multil̄inear mappings
KW - numerical index
KW - Numerical radius
KW - symmetric multilinear mappings
UR - http://www.scopus.com/inward/record.url?scp=84945218601&partnerID=8YFLogxK
U2 - 10.2989/16073606.2015.1068236
DO - 10.2989/16073606.2015.1068236
M3 - Article
AN - SCOPUS:84945218601
SN - 1607-3606
VL - 39
SP - 153
EP - 166
JO - Quaestiones Mathematicae
JF - Quaestiones Mathematicae
IS - 2
ER -