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It is shown that the sum and the product of two commuting Banach space operators with Dunford’s property have the single-valued extension property.
Most mammalian tissues are organized into a hierarchical structure of stem,
progenitor, and differentiated cells. Tumors exhibit similar hierarchy, even if
it is abnormal in comparison with healthy tissue. In particular, it is believed
that a small population of cancer stem cells drives tumorigenesis in certain
malignancies. These cancer stem cells are derived from transformed stem cells or
mutated progenitors that have acquired stem-cell qualities, specifically the
ability to self-renew. Similar...
Let be a bounded operator on a complex Banach space . If is an open subset of the complex plane such that is of Kato-type for each , then the induced mapping has closed range in the Fréchet space of analytic -valued functions on . Since semi-Fredholm operators are of Kato-type, this generalizes a result of Eschmeier on Fredholm operators and leads to a sharper estimate of Nagy’s spectral residuum of . Our proof is elementary; in particular, we avoid the sheaf model of Eschmeier and...
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