TY - JOUR

T1 - Biseparating linear maps between continuous vector-valued function spaces

AU - Gau, Hwa Long

AU - Jeang, Jyh Shyang

AU - Wong, Ngai Ching

PY - 2003/2

Y1 - 2003/2

N2 - Let X, Y be compact Hausdorff spaces and E, F be Banach spaces. A linear map T: C(X, E) → C(Y, F) is separating if Tf, Tg have disjoint cozeroes whenever f, g have disjoint cozeroes. We prove that a biseparating linear bijection T (that is, T and T-1 are separating) is a weighted composition operator Tf = h · f ο φ Here, h is a function from Y into the set of invertible linear operators from E onto F, and φ is a homeomorphism from Y onto X. We also show that T is bounded if and only if h (y) is a bounded operator from E onto F for all y in Y. In this case, h is continuous with respect to the strong operator topology.

AB - Let X, Y be compact Hausdorff spaces and E, F be Banach spaces. A linear map T: C(X, E) → C(Y, F) is separating if Tf, Tg have disjoint cozeroes whenever f, g have disjoint cozeroes. We prove that a biseparating linear bijection T (that is, T and T-1 are separating) is a weighted composition operator Tf = h · f ο φ Here, h is a function from Y into the set of invertible linear operators from E onto F, and φ is a homeomorphism from Y onto X. We also show that T is bounded if and only if h (y) is a bounded operator from E onto F for all y in Y. In this case, h is continuous with respect to the strong operator topology.

UR - http://www.scopus.com/inward/record.url?scp=0037303297&partnerID=8YFLogxK

U2 - 10.1017/s1446788700003153

DO - 10.1017/s1446788700003153

M3 - 期刊論文

AN - SCOPUS:0037303297

SN - 1446-7887

VL - 74

SP - 101

EP - 109

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 1

ER -