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Is there a "right" definition of the nuclear operator in the nonlinear framework ? Of course, such an operator must be compact, while a linear operator should be "nonlinearly" nuclear iff it is nuclea …

Is this little toy known ? Let $E$ be some Banach space, and let $K$ be the closed unit ball of its dual, endowed with the weak-star topology. Also, let $j:E$ $\rightarrow$ $C(K)$ be the natural embe …

Let $E$ be an infinite dimensional Banach space, let $E^{\ast}$ denote its continuous (i.e., Banach space) dual, and let $E'$ be its algebraic dual. Clearly, $E^{\ast}$ is a proper vector subspace of …

Let $E$ be an arbitrary Banach space and let $T:E^{*}\rightarrow\ell^{2}$ be a linear continuous operator. Is it true that $T$ must be the $so$-limit (i.e., limit w.r.t. the strong operator topology) …

Let $K$ be the closed unit ball of $C[0,1]$, and let $f$ in $C(K,\mathbb{\, R})$. Is it true that there exists an infinite dimensional reflexive subspace $E$ of $C[0,1]$ s.t. $f(K\cap E)$ is bounded ? …

Let E be a normed space, and let $T$:E * $\rightarrow$ E * be a nonlinear operator. Suppose that : 1) $T$ is continuous from (E *, ||.||) to itself (i.e., it is norm-continuous). and 2) $T$ is co …

Let $E$ be a real linear space, endowed with a non-degenerate symmetric bilinear form $(.,.)$. Suppose that the [indefinite] inner product space $(E,(.,.))$ satisfies the following [sequential] prope …

Is the following result true: the Hilbert space $\ell^{2}\left(2^{\Gamma}\right)$ is a quotient of $\ell^{\infty}\left(\Gamma\right)$ for any uncountable $\Gamma$ ? [I think it is, but cannot remember …

The question below is related to the classical Browder-Goehde-Kirk fixed point theorem. Let $K$ be the closed unit ball of $\ell^{2}$, and let $T:K\rightarrow K$ be a mapping such that $$\Vert Tx-Ty\V …