Unilateral Shift Homework: Compute SS*, S*S, S^nS^(*n), S^(*n)S^n

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SUMMARY

The discussion centers on the computation of operators related to the unilateral shift, specifically SS*, S*S, S^n S^(*n), and S^(*n)S^n. Participants emphasize the importance of understanding the unilateral shift operator, which is a fundamental concept in functional analysis. The discussion references Wikipedia as a resource for foundational knowledge on unilateral shifts, indicating its relevance for those unfamiliar with the topic.

PREREQUISITES
  • Understanding of operator theory in functional analysis
  • Familiarity with the concept of unilateral shift operators
  • Basic knowledge of Hilbert spaces
  • Experience with linear algebra and matrix representations
NEXT STEPS
  • Research the properties of unilateral shift operators in functional analysis
  • Study the adjoint operator and its significance in operator theory
  • Learn about Hilbert space theory and its applications
  • Explore examples of operator computations involving SS* and S*S
USEFUL FOR

Students and professionals in mathematics, particularly those studying functional analysis, linear algebra, or operator theory, will benefit from this discussion.

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Homework Statement


Let S be the unilateral shift and compute SS^* and S^*S. Also compute S^n S^(*n) and S^(*n)S^n


Homework Equations





The Attempt at a Solution



First what is meant by unilateral shift?
 
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