By Ivan G. Todorov, Lyudmila Turowska

This quantity contains the complaints of the convention on Operator thought and its purposes held in Gothenburg, Sweden, April 26-29, 2011. The convention used to be held in honour of Professor Victor Shulman at the party of his sixty fifth birthday. The papers integrated within the quantity disguise a wide number of issues, between them the idea of operator beliefs, linear preservers, C*-algebras, invariant subspaces, non-commutative harmonic research, and quantum teams, and replicate fresh advancements in those components. The publication involves either unique study papers and top of the range survey articles, all of which have been conscientiously refereed.

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

**Sample text**

The answer is positive if ???? is contained in a ﬁnite von Neumann algebra ℳ. A key part of the proof of this in [3] is the following technical result. 1. Let ℳ be a von Neumann algebra with a faithful, ﬁnite, normal trace ???? , and let ???? ⊆ ℳ be a closed subalgebra which is commutative and amenable. Let Φ???? denote the character space of ????, and let G???? : ???? → ????0 (Φ???? ) denote the Gelfand transform. Then G???? is injective with dense range, and there is a bounded 42 Y. Choi linear map ???? : ????0 (Φ???? ) → ????1 (ℳ, ???? ) which extends the inclusion ???? → ℳ, in the sense that the diagram G???? ???? ⏐ ⏐ ????0 (Φ???? ) inclusion −−−−−−−→ ???? −−−−→ ℳ ⏐ ⏐ inclusion (5) ????1 (ℳ, ???? ) commutes.

Then ???????????? (???????? ) (????) is a closed ideal of ???????? (???????? ). 1]). Let ???? ∈ ℤ with ???? ≥ 0 and 0 ≤ ???? < ????????+1 . Then ( ) ( ) dist (z − 1)???? +1 , ???????????? (????) (???????? ) ≤ 2 tan ????2+1 ???? ????1 (???? ), where, here and subsequently, ????1 (???? ) = 3 ???? ???? +1 ( ∑ ) ???? +1 ???? ???? . 3. 2. Let ???? ∈ ℤ with ???? ≥ 0 and 0 ≤ ????1 , ????2 < ????????+1 . Then ( ) dist (z1 − 1)???? +1 (z2 − 1)???? +1 , ???????????? (????2 ) (????????1 × ???? ∪ ???? × ????????2 ) ( ) ( ) ( ) ( )) ( ≤ 2 tan ????2+1 ????1 + 2 tan ????2+1 ????2 + 4 tan ????2+1 ????1 tan ????2+1 ????2 ????2 (???? ).

0⎦ ℋ2????+1 ⊖ ℋ2???? 0 ℋ ⊖ ℋ2????+1 It is easily checked that for each ????, we have ????2???? = ???????? and ???????? ????????+1 = ???????? = ????????+1 ???????? (consider the cases of odd and even ???? separately). The latter property implies, by induction, that ???????? ???????? = ????min(????,????) = ???????? ???????? for all ????, ???? ∈ ℕ. 4. Hence it is a boundedly approximately contractible Banach algebra. 1. 4. n. basis (???????? )????≥0 , and deﬁne ℋ???? = lin(????0 , . . , ???????? ), so that each ????2???? is a scalar. 1. Using that lemma, we thus obtain an example of a compact operator on Hilbert space which generates a non-amenable, boundedly approximately contractible algebra.