TY - JOUR

T1 - Holomorphic mappings of domains in operator spaces

AU - Harris, Lawrence A.

PY - 1997/12

Y1 - 1997/12

N2 - Throughout, most of the domains we have considered are circular domains in the sense of [13]. Specifically, if 2Θ is a closed complex subspace of of ℒ(H, K), a circular domain in 2Θ is a set of the form D = {Z ∈ 2Θ : Z* EZ + 2 Re F* Z + G < 0}, where E ∈ ℒ(K), F ∈ ℒ(H, K), G ∈ ℒ(H) and both E and G are self adjoint. For example, 2Θ0 is a circular domain since 2Θ0 = {Z ∈ 2Θ : Z*Z - I < 0}. The circular domains of the complex plane are any open disc, the exterior of any open disc, any open half-plane, any punctured plane, the entire plane and the empty set. (This terminology is taken from [24, p. 57] and [16, p. 464]. A different definition, which is also referred to as "circled," is given in [19, p. 113] and [2, p. 104].) One of our main objectives has been to determine the automorphisms of circular domains and to discover circular domains that are homogeneous. Linear fractional transformations have served as a basic tool.

AB - Throughout, most of the domains we have considered are circular domains in the sense of [13]. Specifically, if 2Θ is a closed complex subspace of of ℒ(H, K), a circular domain in 2Θ is a set of the form D = {Z ∈ 2Θ : Z* EZ + 2 Re F* Z + G < 0}, where E ∈ ℒ(K), F ∈ ℒ(H, K), G ∈ ℒ(H) and both E and G are self adjoint. For example, 2Θ0 is a circular domain since 2Θ0 = {Z ∈ 2Θ : Z*Z - I < 0}. The circular domains of the complex plane are any open disc, the exterior of any open disc, any open half-plane, any punctured plane, the entire plane and the empty set. (This terminology is taken from [24, p. 57] and [16, p. 464]. A different definition, which is also referred to as "circled," is given in [19, p. 113] and [2, p. 104].) One of our main objectives has been to determine the automorphisms of circular domains and to discover circular domains that are homogeneous. Linear fractional transformations have served as a basic tool.

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U2 - 10.1016/S0362-546X(97)00244-7

DO - 10.1016/S0362-546X(97)00244-7

M3 - Article

AN - SCOPUS:0042045464

SN - 0362-546X

VL - 30

SP - 3493

EP - 3503

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 6

ER -