We use the fixed point alternative theorem to prove that, under suitable conditions, every A-valued approximate isometry on a Hilbert C∗-module over the C∗-algebra A can be approximated by a unique A-valued isometry. AMS subject classifications: Primary 39B52, 39B82, 46B04, 46L08; Secondary 47H10

A regular operator T on a Hilbert C *-module is defined just like a closed operator on a Hilbert space, with the extra condition that the range of (I + T * T) is dense. Semiregular operators are a slightly larger class of operators that may not have this property. It is shown that, like in the case of regular operators, one can, without any loss in generality, restrict oneself to semiregular op...

X iv :0 90 5. 40 67 v1 [ m at h. FA ] 2 5 M ay 2 00 9 BESSEL TYPE INEQUALITIES IN HILBERT C-MODULES S. S. DRAGOMIR, M. KHOSRAVI AND M. S. MOSLEHIAN Abstract. Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombiari and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C∗-mo...

We prove that an arbitrary (not necessarily countably generated) Hilbert G −A module on a G − C∗ algebra A admits an equivariant embedding into a trivial G−A module, provided G is a compact Lie group and its action on A is ergodic.

It is shown that the metric on union of sets X and Y defines a Hilbert $C^*$ -module over uniform Roe algebra space with fixed dX. A number examples such -modules are described.