### Almost surjective ε-isometries of Banach spaces

We investigate Hyers-Ulam stability of non-surjective ε-isomeries of Banach spaces. We also pose and discuss an open problem.

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We investigate Hyers-Ulam stability of non-surjective ε-isomeries of Banach spaces. We also pose and discuss an open problem.

We introduce the notion of a $g$-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of $g$-fusion frames. Also, we shall describe the concept of frame operator for a pair of $g$-fusion Bessel sequences and some of their properties.