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|Title:||Relative numerical ranges|
|Abstract:||Relying on the ideas of Stampfli  and Magajna  we introduce, for operators S and T on a separable complex Hilbert space, a new notion called the numerical range of S relative to T at r is an element of sigma(vertical bar T vertical bar). Some properties of these numerical ranges are proved. In particular, it is shown that the relative numerical ranges are non-empty convex subsets of the closure of the ordinary numerical range of S. We show that the position of zero with respect to the relative numerical range of S relative to T at parallel to T parallel to gives an information about the distance between the involved operators. This result has many interesting corollaries. For instance, one can characterize those complex numbers which are in the closure of the numerical range of S but are not in the spectrum of S.|
|Appears in Collections:||DM-RI - Artigos em revistas científicas internacionais|
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