<?xml version="1.0" encoding="UTF-8"?><?xml-stylesheet type="text/xsl" href="static/style.xsl"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-09-21T16:14:34Z</responseDate><request verb="GetRecord" identifier="oai:repository.rice.edu:1911/18442" metadataPrefix="dim">https://repository.rice.edu/server/oai/request</request><GetRecord><record><header><identifier>oai:repository.rice.edu:1911/18442</identifier><datestamp>2024-01-11T20:57:42Z</datestamp><setSpec>com_1911_8299</setSpec><setSpec>col_1911_13110</setSpec></header><metadata><dim:dim xmlns:dim="http://www.dspace.org/xmlns/dspace/dim" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:doc="http://www.lyncode.com/xoai" xsi:schemaLocation="http://www.dspace.org/xmlns/dspace/dim http://www.dspace.org/schema/dim.xsd">
   <dim:field mdschema="dc" element="creator">Scroggs, James E.</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="accessioned">2007-08-21T01:07:56Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="available">2007-08-21T01:07:56Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="issued">1957</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="citation">Scroggs, James E.. &amp;quot;On invariant subspaces of a normal operator.&amp;quot; (1957) Diss.,  Rice University.  &amp;lt;a href=&amp;quot;https://hdl.handle.net/1911/18442&amp;quot;&amp;gt;https://hdl.handle.net/1911/18442&amp;lt;/a&amp;gt;.</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="uri">https://hdl.handle.net/1911/18442</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="callno">Thesis Math. 1957 Scroggs</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="abstract">Our principal interest, in the work that follows, is the discovery of conditions on the spectrum of a normal operator which imply that the operator has invariant non-reducing subspaces. We were led to this study by the work of Halmos, Wermer, and Bram.</dim:field>
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   <dim:field mdschema="dc" element="language" qualifier="iso">eng</dim:field>
   <dim:field mdschema="dc" element="rights">Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.</dim:field>
   <dim:field mdschema="dc" element="subject">Mathematics</dim:field>
   <dim:field mdschema="dc" element="title">On invariant subspaces of a normal operator</dim:field>
   <dim:field mdschema="dc" element="type">Thesis</dim:field>
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   <dim:field mdschema="thesis" element="degree" qualifier="department">Mathematics</dim:field>
   <dim:field mdschema="thesis" element="degree" qualifier="discipline">Natural Sciences</dim:field>
   <dim:field mdschema="thesis" element="degree" qualifier="grantor">Rice University</dim:field>
   <dim:field mdschema="thesis" element="degree" qualifier="level">Doctoral</dim:field>
   <dim:field mdschema="thesis" element="degree" qualifier="name">Doctor of Philosophy</dim:field>
   <dim:field mdschema="others" element="access-status">open.access</dim:field>
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