# Journal of the Ramanujan Mathematical Society

Volume 36, Issue 1, March 2021 pp. 85–91.

Best approximations, distance formulas and orthogonality in C{*}-algebras

**Authors**:
Priyanka Grover and Sushil Singla

**Author institution:**Department of Mathematics, Shiv Nadar University, NH-91, Tehsil Dadri, Gautam Buddha Nagar, U.P. 201314, India

**Summary: **
For a unital C{*}-algebra A and a subspace B of A, a characterization for a best approximation to an
element of A in B is obtained. As an application, a formula for the distance of an element of A from B has been
obtained, when a best approximation of that element to B exists. Further, a characterization for Birkhoff-James
orthogonality of an element of a Hilbert C{*}-module to a subspace is obtained.

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