Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...

We develop methods that construct an optimal set of vectors with a specified inner product structure, from a given set of vectors in a complex Hilbert space. The optimal vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors. Four special cases are considered. In the first, the constructed vectors are orthonormal. In the s...

We extend the reach of functional encryption schemes that are provably secure under simpleassumptions against unbounded collusion to include function-hiding inner product schemes.Our scheme is a private key functional encryption scheme, where ciphertexts correspond tovectors ~x, secret keys correspond to vectors ~y, and a decryptor learns 〈~x, ~y〉. Our schemeemploys asymmetr...