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By Ivan G. Todorov, Lyudmila Turowska

This quantity includes the court cases of the convention on Operator thought and its purposes held in Gothenburg, Sweden, April 26-29, 2011. The convention was once held in honour of Professor Victor Shulman at the party of his sixty fifth birthday. The papers incorporated within the quantity cover a huge number of issues, between them the speculation of operator beliefs, linear preservers, C*-algebras, invariant subspaces, non-commutative harmonic research, and quantum teams, and reflect fresh advancements in those components. The publication involves both original learn papers and top of the range survey articles, all of which were carefully refereed. ​

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Extra info for Algebraic Methods in Functional Analysis: The Victor Shulman Anniversary Volume

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Shulman. The author thanks the conference organizers for an enjoyable and stimulating meeting. He would also like to thank Mikael de la Salle and Jesse Peterson for useful discussions on the MathOverflow website. Finally, the author thanks the anonymous referee for his or her suggestions and corrections: in particular, the requests for clarification of the original version of Section 2, which led to the repair and improvement of some incomplete arguments. The work here was partially supported by NSERC Discovery Grant 4021532011.

8). Suppose that ????1 and ????2 are commuting representations of ???? on ???? and ???? is a representation of ???? on ???? such that ∥????1 (????????)∥, ∥????2 (????????)∥, ∥???? (????????)∥ = ????(∣????∣???? ) as ∣????∣ → ∞ (???? ∈ ????) for some ???? ≥ 0. If ???? ∈ ℬ(????, ???? ) is such that sp(????, ????????) ⊂ sp(????1 , ????) ∪ sp(????2 , ????) (???? ∈ ????), then ???? ∑ ????1 +????2 (−1) ????1 ,????2 =0 ( ???? ????1 )( ) ???? ???? (????)2???? −(????1 +????2 ) ????????1 (????)????1 ????2 (????)????2 = 0 (???? ∈ ????) ????2 for each ???? > 2????. Proof. Let ???? ∈ ????. We consider the continuous linear map Φ???? : ???????? (????) → ???? (????, ????) and the continuous trilinear map ???? : ???????? (????) × ???????? (????) × ???????? (????) → ℬ(????, ???? ) defined by +∞ ∑ Φ???? (???? ) = ????ˆ(????)???????????? (???? ∈ ???????? (????)) ????=−∞ and ( ( ( ) ) ) ???????? (????, ????, ℎ) = ????˜ Φ???? (???? ) ∘ ???? ∘ ???? ˜1 Φ???? (????) ∘ ???? ˜2 Φ???? (ℎ) (????, ????, ℎ ∈ ???????? (????)), respectively.

347 (2008), 472–481. [2] J. Alaminos, M. Breˇsar, J. R. Villena, Maps preserving zero products, Studia Math. 193 (2) (2009), 131–159. [3] J. Alaminos, M. Breˇsar, J. R. Villena, Characterizing Jordan maps on ???? ∗ -algebras through zero products, Proc. Edinb. Math. Soc. 53(3) (2010), 543–555. [4] J. Alaminos, J. R. Villena, Zero product preserving maps on Banach algebras of Lipschitz functions, J. Math. Anal. Appl. 369 (2010), 94–100. [5] J. Alaminos, J. R. Villena, Operators shrinking the Arveson spectrum, Publ.

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