About: Unilateral shift operator

Property	Value
dbp:mathStatement	Let be the open unit disk, the closed unit disk, and the unit circle. * The spectrum of is . * The point spectrum of is empty: . * The approximate point spectrum of is the unit circle: . (en)
dbp:name	Spectrum of the forward shift (en)
dbp:proof	To show , use the matrix representation of , and note that it is bounded iff . To show , directly show that implies . To show , note that for any with , so . Conversely, for any , construct the following unit vectorthen , which converges to 0 at . (en)
dbp:title	Proof (en)
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Math_theorem dbt:Math_proof dbt:Expert_needed dbt:Reference_page dbt:Reflist dbt:Short_description
dct:subject	dbc:Operator_theory dbc:Linear_operators dbc:Hilbert_spaces
rdfs:label	Unilateral shift operator (en)
prov:wasDerivedFrom	wikipedia-en:Unilateral_shift_operator?oldid=1312028686&ns=0
foaf:isPrimaryTopicOf	wikipedia-en:Unilateral_shift_operator
is foaf:primaryTopic of	wikipedia-en:Unilateral_shift_operator