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 -