Almost minimal orthogonal projections

On Almost Orthogonal Frames

Almost Orthogonal Submatrices of an Orthogonal Matrix

Let t ≥ 1 and let n, M be natural numbers, n < M. Let A = (a i,j) be an n × M matrix whose rows are orthonormal. Suppose that for all j M n · n i=1 a 2 i,j 1/2 ≤ t.

Products of Orthogonal Projections

We give a characterization of operators on a separable Hilbert space of norm less than one that can be represented as products of orthogonal projections and give an estimate on the number of factors. We also describe the norm closure of the set of all products of orthogonal projections.

Minimal Almost Convexity

In this article we show that the Baumslag-Solitar group BS(1, 2) is minimally almost convex, or MAC. We also show that BS(1, 2) does not satisfy Poénaru’s almost convexity condition P (2), and hence the condition P (2) is strictly stronger than MAC. Finally, we show that the groups BS(1, q) for q ≥ 7 and Stallings’ non-FP3 group do not satisfy MAC. As a consequence, the condition MAC is not a c...

On Minimal and Almost-Minimal Linear Codes

Minimal linear codes are such that the support of every codeword does not contain the support of another linearly independent codeword. Such codes have applications in cryptography, e.g. to secret sharing and secure two-party computations. We pursue here the study of minimal codes and construct infinite families with asymptotically non-zero rates. We also introduce a relaxation to almost minima...