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| Compatibility and Schur Complements of Operators on Hilbert C*-Module |
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Citation： |
Xiaochun FANG,Jing YU.Compatibility and Schur Complements of Operators on Hilbert C*-Module[J].Chinese Annals of Mathematics B,2011,32(1):69~88 |
| Page view： 1927
Net amount： 1407 |
Authors： |
Xiaochun FANG; Jing YU; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10771161, 11071188). |
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| Abstract： |
Let $E$ be a Hilbert $C^{*}$-module, and
$\mathscr{S}$ be an orthogonally complemented closed submodule of
$E$. The authors generalize the definitions of
$\mathscr{S}$-complementability and $\mathscr{S}$-compatibility for
general (adjointable) operators from Hilbert space to Hilbert
$C^{*}$-module, and discuss the relationship between each other.
Several equivalent statements about $\mathscr{S}$-complementability
and $\mathscr{S}$-compatibility, and several representations of
Schur complements of $\mathscr{S}$-complementable operators
(especially,
of $\mathscr{S}$-compatible operators and of positive
$\mathscr{S}$-compatible operators) on a Hilbert $C^{*}$-module are obtained. In addition,
the quotient property for Schur complements of matrices
is generalized to the quotient property for Schur complements of
$\mathscr{S}$-complementable operators and
$\mathscr{S}^*$-complementable operators on a Hilbert $C^*$-module. |
Keywords： |
Hilbert C
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-module, Compatibility, Complementability,
Schur complement, Quotient property |
Classification： |
46L08, 47A64, 47A07 |
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