Hermitian Geometry on Resolvent Set
Hermitian Geometry on Resolvent Set
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DOI：
10.1007/978-3-319-72449-2_8
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
R. Douglas;Rongwei Yang
中科院分区：
文献类型：
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作者：
R. Douglas;Rongwei Yang
For a tupleof elements in a unital Banach algebra, itsprojective joint spectrum P(A) is the collection ofsuch thatis not invertible. It is known that the-valued 1-formcontains much topological information about the joint resolvent setPc(A). This paper studies geometric properties ofPc(A) with respect to Hermitian metrics defined through the-valuedfundamental formand its coupling withfaithfulstatesφon, i.e.,φ(ΩA). The connection between the tupleAand the metric is the main subject of this paper. In particular, it shows that the Kählerness of the metric is tied with the commutativity of the tuple, and its completeness is related to the Fuglede–Kadison determinant.
