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- W2117505974 abstract "A new approach to the Lance-Blecher theorem is presented resting on the interpretation of elements of Hilbert C*-module theory in terms of multiplier theory of operator C*-algebras: The Hilbert norm on a Hilbert C*-module allows to recover the values of the inducing C*-valued inner product in a unique way, and two Hilbert C*-modules {M_1, _1}, {M_2, _2} are isometrically isomorphic as Banach C*-modules if and only if there exists a bijective C*-linear map S: M_1 --> M_2 such that the identity _1 equiv _2 is valid. In particular, the values of a C*-valued inner product on a Hilbert C*-module are completely determined by the Hilbert norm induced from it. In addition, we obtain that two C*-valued inner products on a Banach C*-module inducing equivalent norms to the given one give rise to isometrically isomorphic Hilbert C*-modules if and only if the derived C*-algebras of ''compact'' module operators are *-isomorphic. The involution and the C*-norm of the C*-algebra of ''compact'' module operators on a Hilbert C*-module allow to recover its original C*-valued inner product up to the following equivalence relation: _1 sim _2 if and only if there exists an invertible, positive element $a$ of the center of the multiplier C*-algebra M(A) of A such that the identity _1 equiv a cdot _2 holds." @default.
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- W2117505974 date "1997-01-01" @default.
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- W2117505974 title "A Multiplier Approach to the Lance-Blecher Theorem" @default.
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- W2117505974 doi "https://doi.org/10.4171/zaa/778" @default.
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