TY - JOUR
T1 - Matrix symbol of order two for some banach algebras
AU - Krupnik, Naum
AU - Spigel, Yafim
PY - 2001
Y1 - 2001
N2 - Two classes of Banach algebras which admit a matrix symbol of order 2 are described, and an explicit form of the symbol is obtained. Also we describe all polynomials F(X, Y) and F(X, Y, Z) such that the norms of polynomials F(B, B*) ( when B2 = 0) and F(S, W, W*) (when S2 = I, W2 = 0, S* = S) depend only on the polynomial F and on the norms ∥B∥, ∥W∥. Applications to Banach algebras generated by singular integral operators and some their perturbations are considered.
AB - Two classes of Banach algebras which admit a matrix symbol of order 2 are described, and an explicit form of the symbol is obtained. Also we describe all polynomials F(X, Y) and F(X, Y, Z) such that the norms of polynomials F(B, B*) ( when B2 = 0) and F(S, W, W*) (when S2 = I, W2 = 0, S* = S) depend only on the polynomial F and on the norms ∥B∥, ∥W∥. Applications to Banach algebras generated by singular integral operators and some their perturbations are considered.
UR - http://www.scopus.com/inward/record.url?scp=0035652016&partnerID=8YFLogxK
U2 - 10.1007/bf01198141
DO - 10.1007/bf01198141
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AN - SCOPUS:0035652016
SN - 0378-620X
VL - 40
SP - 465
EP - 480
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
IS - 4
ER -