Throughout this note, X and Y will stand for locally compact Hausdorff spaces, and E and F for Banach spaces. Let C_0(X, E) and C_0(Y, F) be the Banach spaces of continuous E-valued and F-valued functions vanishing at infinity defined on X and Y respectively and endowed with the supremum norm ‖·‖_∞. Let K denote the field of real or complex numbers. If E = F = K, then we will write C_0(X) and C_0(Y) (C(X) and C(Y) if X, Y are compact).
展开▼
机译：在整个说明中，X和Y代表局部紧凑的Hausdorff空间，E和F代表Banach空间。令C_0（X，E）和C_0（Y，F）为连续的E值和F值函数的Banach空间，它们分别在X和Y上定义的无穷远处消失，并赋予最高范数”·”_∞。令K表示实数或复数的字段。如果E = F = K，则我们将写C_0（X）和C_0（Y）（如果X，Y为紧凑型，则C（X）和C（Y））。
展开▼
