Abstract:
The Barth-Van de Ven-Tyurin-Sato Theorem states that any finite-rank vector bundle on the complex projective ind-space $\mathbf{P}^\infty$ is isomorphic to a direct sum of line bundles. We establish sufficient conditions on a locally complete linear ind-variety $\mathbf{X}$ which ensure that the same result holds on $\mathbf{X}$. We then exhibit natural classes of locally complete linear ind-varieties which satisfy these sufficient conditions.
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