In this paper, we establish some new results in ultra Bessel se- quences and ultra Bessel sequences of subspaces. Also, we in- vestigate ultra Bessel sequences in direct sums of Hilbert spaces. Specially, we show that f( fi; gi)g1 i=1 is a an ultra Bessel sequence for Hilbert space H K if and only if f fig1 i=1 and fgig1 i=1 are ultra Bessel sequences for Hilbert spaces H and K; respectively.
