The authors prove several infinite dimensional generalizations of classical finite dimensional theorems. First is the version of Kwack's theorem: Theorem 1.1. Let \(X\) be a hyperbolic Banach analytic space and \(f:Z\setminus H\to X\) a holomorphic map, where \(H\) is a hypersurface in a complex Banach manifold \(Z\). Assume that for every \(z\in H\) there exists a sequence \(\{z_n\}\subset Z\setminus H\) converging to \(Z\), such that \(\{f(z_k)\}\) converges in \(X\). Then \(f\) extends holomorphically to \(Z\). One more result is: Theorem 2.1. Let \(X\) be a Banach analytic space which is an increasing union of pseudoconvex domains. Assume that \(X\) contains no complex lines. Then \(X\) has the Hartogs extension property. The latter means that every holomorphic map from a Riemann domain \(\Omega\) over a Banach space \(B\), with Schauder basis, into \(X\) can be extended holomorphically to the envelope of holomorphy \(\widehat\Omega\) of \(\Omega\).