Stability of isometries in $p$-Banach spaces

Stability of generalized QCA-functional equation in P-Banach spaces

In  this paper, we investigate the generalizedHyers-Ulam-Rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{Z}-{0,pm1}$) in $p-$Banach spaces.

Partial Isometries on Banach Spaces

stability of generalized qca-functional equation in p-banach spaces

in  this paper, we investigate the generalizedhyers-ulam-rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{z}-{0,pm1}$) in $p-$banach spaces.

Isometries on Extremely Non-complex Banach Spaces

We construct an example of a real Banach space whose group of surjective isometries reduces to ± Id, but the group of surjective isometries of its dual contains the group of isometries of a separable infinite-dimensional Hilbert space as a subgroup. To do so, we present examples of extremely non-complex Banach spaces (i.e. spaces X such that ‖ Id+T ‖ = 1+‖T ‖ for every bounded linear operator T...

Stability in Banach Spaces

Many questions in Banach space theory are of the type: Let X be an infinite dimensional Banach space. Let (P) be a property. Does X contain a closed infinite dimensional subspace Y with (P)? Sometimes the question takes the form: If X has a certain property (Q), does X contain Y having (P)? Of course the answers and solutions (if known) depend upon the particular properties involved. But there ...