In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(...In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(p) less than or equal to parallel to F(0)parallel to(p) + C-p (1 - parallel to A parallel to)(-2) [GRAPHICS]展开更多
Suppose H is a complex Hilbert space, A H(Δ) denotes the set of all analytic operator functions on Δ, and the set N H(Δ)=｛f(z)｜f(z) is an analytic operator function on the open uint disk Δ, f(z)f(w)=f(w)f(z),f...Suppose H is a complex Hilbert space, A H(Δ) denotes the set of all analytic operator functions on Δ, and the set N H(Δ)=｛f(z)｜f(z) is an analytic operator function on the open uint disk Δ, f(z)f(w)=f(w)f(z),f *(z)f(z)=f(z)f *(z),z,w∈Δ｝. The note proves that if f(z)∈N H(Δ),(or A H(Δ))‖f(z)‖≤1,z∈Δ then‖f′(T)‖≤(1-‖T‖ 2) -1 ‖I-f *(T)f(T)‖ 12 ‖I-f(T)f *(T)‖ 12 , where T∈L(H)(orT *T=TT *,respectively),‖T‖<1,Tf=fT.展开更多
文摘In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(p) less than or equal to parallel to F(0)parallel to(p) + C-p (1 - parallel to A parallel to)(-2) [GRAPHICS]
基金Education Foundation of Henan Province(981 1 0 0 1 2 )
文摘Suppose H is a complex Hilbert space, A H(Δ) denotes the set of all analytic operator functions on Δ, and the set N H(Δ)=｛f(z)｜f(z) is an analytic operator function on the open uint disk Δ, f(z)f(w)=f(w)f(z),f *(z)f(z)=f(z)f *(z),z,w∈Δ｝. The note proves that if f(z)∈N H(Δ),(or A H(Δ))‖f(z)‖≤1,z∈Δ then‖f′(T)‖≤(1-‖T‖ 2) -1 ‖I-f *(T)f(T)‖ 12 ‖I-f(T)f *(T)‖ 12 , where T∈L(H)(orT *T=TT *,respectively),‖T‖<1,Tf=fT.
