Ultra Bessel sequences in direct sums of Hilbert spaces

Document Type: Research Paper


1 University of Mohaghegh Ardabili

2 University of Maragheh


In this paper, we establish some new results in ultra Bessel sequences and ultra Bessel sequences of subspaces. Also, we investigate ultra Bessel sequences in direct sums of Hilbert spaces. Specially, we show that {( fi, gi)}i=1 is a an ultra Bessel sequence for Hilbert space H ⊕ K if and only if { fi}i=1 and {gi}i=1 are ultra Bessel sequences for Hilbert spaces H and K, respectively.


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