PERMUTATIONS AND WOVEN g-FRAMES

Two g-frames {3i }i is an element of I and {0i }i is an element of I for the Hilbert space are called woven if for each subset sigma of . the weaving {3i }i is an element of sigma boolean OR {0i }i is an element of sigma c is a g-frame for The aim of this paper is to consider the reordered families of a g-frame {3i }i is an element of I with various woven problems. First, we state some useful results for exact g-frames and excess of g-frames. Then for sigma subset of . we consider the families of weavings {3i }i is an element of sigma boolean OR {3 pi(i)}i is an element of sigma c where pi is a permutation function on . and obtain some new conclusions. Lastly, we give relations of reordered weavings and operators, especially g-frame operators.