NORNIALS, SUBNORMALS AND AN OPEN QUESTION

作者：Szafraniec Franciszek Hugon^*

来源：Operators and Matrices, 2010, 4(4): 485-510.

• Bounded operator
• unbounded operator
• normal operator
• *-cyclic operator
• cyclic operator
• quasinormal operator
• subnormal operator
• minimality of normal extension
• minimality of spectral type
• semispectral measure
• elementary spectral measure
• minimality of cyclic type
• uniqueness of extensions
• invariant domain
• complex moment problem
• determinacy of measure
• ultradeterminacy of measure
• vector of determinacy
• vector of ultradeterminacy
• creation operator
• quantum harmonic oscillator
• Segal-Bargmann space
• analytic model
• reproducing kernel Hilbert space
• integrability of RKHS

An acute look at basic facts concerning unbounded subnormal operators is taken here. These operators have the richest structure and are the most exciting among the whole family of beneficiaries of the normal ones. Therefore, the latter must necessarily be taken into account as the reference point for any exposition of subnormality. So as to make the presentation more appealing a kind of comparative survey of the bounded and unbounded case has been set forth.
This piece of writing serves rather as a practical guide to this largely impenetrable territory than an exhausting report.

• 出版日期2010-12