منابع مشابه
A ZPP Lifting Theorem
The complexity class ZPP (corresponding to zero-error randomized algorithms with access to one NP oracle query) is known to have a number of curious properties. We further explore this class in the settings of time complexity, query complexity, and communication complexity. r For starters, we provide a new characterization: ZPP equals the restriction of BPP where the algorithm is only allowed t...
متن کاملA Lifting Theorem for Symmetric Commutants
Let T1, . . . , Tn ∈ B(H) be bounded operators on a Hilbert space H such that T1T ∗ 1 + · · · + TnT ∗ n ≤ IH. Given a symmetry j on H, i.e., j2 = j∗j = IH, we define the j-symmetric commutant of {T1, . . . , Tn} to be the operator space {A ∈ B(H) : TiA = jATi, i = 1, . . . , n}. In this paper we obtain lifting theorems for symmetric commutants. The result extends the Sz.-Nagy–Foiaş commutant li...
متن کاملNotes on the Lifting Theorem
We have seen that the proof of existence of inverses for elements of Ext(X) can be based on a lifting theorem for (completely) positive maps of C(X) into a quotient C∗-algebra of the form E/K, where E ⊆ B(H) is a C∗-algebra containing the compact operators K. That argument works equally well for arbitrary C∗-algebras in place of C(X) whenever a completely positive lifting exists. Thus we are le...
متن کاملLifting map automorphisms and MacBeath's theorem
The purpose of the present note is essentially twofold . First we wish to indicate how coverings of maps can be obtained easily and in a direct way by using a cohomological construction. Secondly, we wish to apply this construction to obtain in an explicit way infinitely many examples of finite maps which are extremal in the sense of having 84(g− 1) automorphisms, where g is the genus of the ma...
متن کاملA Simultaneous Lifting Theorem for Block Diagonal Operators
Stampfli has shown that for a given T £ B(H) there exists a K £ C(H) so that o(T + K) = ow(T). An analogous result holds for the essential numerical range We(T). A compact operator K is said to preserve the Weyl spectrum and essential numerical range of an operator T £ B(H) if o(T + K) = o„(T) and W(T + K)= We(T). Theorem. For each block diagonal operator T, there exists a compact operator K wh...
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ژورنال
عنوان ژورنال: ACM Transactions on Computation Theory
سال: 2020
ISSN: 1942-3454,1942-3462
DOI: 10.1145/3428673