On Functions of Negative Type on the Olshanski Spherical Pair (SL(∞), SU(∞))

Key Points

• The research aims to establish the boundedness of biinvariant functions on the Olshanski spherical pair.
• Utilized a generalized Bochner type representation for Olshanski spherical pairs
• Analyzed continuous functions on SL(∞)
• Focused on functions with negative type
• Investigated the implications of biinvariance under SU(∞)
• Demonstrated that every SU-bi-invariant continuous function of negative type is bounded
• Provided evidence for the relationship between negative type and boundedness
• Established key results in the context of infinite dimensional analysis