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Banach Spaces with respect to Operator-Valued Norms
Yun-Su Kim
We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner prod…
Operator-Valued Norms
Yun-Su Kim
We introduce two kinds of operator-valued norms. One of them is an -valued norm. The other one is an -valued norm. We characterize the completeness with respect to a…
A Shift Operator on L(H^2)
Yun-Su Kim
We give definitions and some properties of the shift operator S_{L(H^2)} and multiplication operator on L(H^2). In addition, we obtain some properties of the commutant of the shift…
A Generalization of Beurling's Theorem and Quasi-Inner Functions
Yun-Su Kim
We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator on a vector-valued Hardy space is generated by a…