A characterization for ∗-isomorphisms in an indefinite inner product space |
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| Authors: | K.C. Sivakumar K. Kamaraj |
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| Affiliation: | a Department of Mathematics, Indian Institute of Technology, Madras, Chennai 600 036, India
b Department of Mathematics, Tagore Engineering College, Rathinamangalam, Chennai 600 048, India |
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| Abstract: | Let H1 and H2 be indefinite inner product spaces. Let L(H1) and L(H2) be the sets of all linear operators on H1 and H2, respectively. The following result is proved: If Φ is [∗]-isomorphism from L(H1) onto L(H2) then there exists  such that Φ(T)=cUTU[∗] for all T∈L(H1) with UU[∗]=cI2, U[∗]U=cI1 and c=±1. Here I1 and I2 denote the identity maps on H1 and H2, respectively. |
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| Keywords: | Indefinite inner product &lowast -Isomorphism |
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