共查询到10条相似文献,搜索用时 15 毫秒
1.
In this paper it is proved that if T is a bounded linear operator on a Hilbert space H and λ(?)c1(W(T)), where cl(W(T)) is the closure of W(T)={(Tx, x); x∈H, ‖x‖ =1}, then T is normal iff Uλ=(T-λ)*-1 (T-λ) is hyponormal and T is hyponormal iff Uλ=(T-λ)*-1 (T-λ) is normaliod. 相似文献
2.
关于非线性泛函的一个问题 总被引:2,自引:0,他引:2
Suppose that H is a Hilbert space, D is a convex closed set inis a functioal, f(x)=1/2‖x‖2-g(x). Suppose that the minimum of f(x) withrespect to D is attained at x0∈D and f(x) has a bounded linear Gateaux differential at x0. In this paper we prove that f(x0) is a critical value of f(x) when and only when g′(x0)∈ID(x0)={(1-λ)x0+λy|y∈D.λ≥0}. 相似文献
3.
In this paper, a derivation δAB mapping into a ideal I of B(H) is considered, when A,B ∈B(H) and I is a norm ideal. If Ran(δAB)?I, let δAB:B(H)→I denote the induced operator and let λ be the scalar such that A- λ∈I, B-λ∈I, we estimate the norm of δAB as follows‖A-λ‖+‖B-λ‖≥‖δAB‖≥‖A- λ‖+‖B-λ‖ when WN(A-λ)∩WN(λ - B)≠?, where WN(A- λ) denotes the normalized maximal numerical range and ‖A-λ‖ denotes the norm of A-λ∈I. In particular when I=Cp(l
p, we prove that ‖δAB‖p=‖A-λ‖p+‖B-λ‖p if and only if ‖A-λ‖=‖A-λ‖p and WN(A-λ)∩WN(λ-B)≠?. At last, some examples show that the estimate as above is exact. 相似文献
4.
Theorem. A mapping x** of X* into sealar field Φ is a linear functional if and only if there exists a μ∈ba(S) such that X**(X*)=∫sx*(s)μ(ds),x*∈X* Theorem. F∈ba(S.Σ)* if and only if there exists a λ∈ba (T) (T is the closed unit sphere of the space B(S,Σ))such that F(μ)=∫(∫st(s)μ(ds))λ(dt),μ∈ba(S,Σ). 相似文献
5.
Hilbert-Schmidt类上的k-拟亚正规算子 总被引:2,自引:0,他引:2
An operator T acting on a Hilbert space H is called k- quasihyponormal if {T} =T*k (T*T-TT*)Tk≥0 . Let A and B be two operators on H, one can obtain an operator τ =τAB on the class l2 of all Hilbert-Schmidt operators on H in such a way that τ(X)=AXB for every X∈l2. In this note the authors show that 相似文献
6.
关于组合合成阵 总被引:2,自引:0,他引:2
We define the rth combinatorial compound Cr*(A) of a matrix A, which can be viewed as the characteristic function of the subset of the rxr submatrices of A which are combinatorially nonsingular. We prove that for 1≤rr*(A)is. We determine the minimum number of 2×2 and 3×3 combinatorially nonsingular submatrices over all n×n fully indecomposable matrices and make a jecture for general r. 相似文献
7.
《数学学报》2012,(4):769-772
<正>On Tame Operators betWeen Non-Archimedean PoWer Series Spaces Wiestaw SLIWA Agnieszka ZIEMKOWSKA Abstract Let P∈{1,∞).We show that any continuous linear operator T from A1(a)to Ap(b)is tame,i.e.,there exists a positive integer C such that supx‖Tx‖k/|x|ck〈∞for every k∈N.Next we prove that a similar result holds for operators from A∞(a)to Ap(b)if and only if the set M_(b,a) of all finite limit points of the double sequence(bi/aj)i,jeN is bounded.Finally we show that the range of every tame operator from A∞(a)to Ao∞(b)has a Schauder basis. 相似文献
8.
Let K be a field, K* be the multiplicative group of nonzero elements of K and S be a subgroup of K*. In this paper we show that S is a group of units of a valuation ring of K if and only if S satisfies the following conditions:1.a∈S implies -a∈S;2. for any a∈K*\S either a+S?S or a-1+S?S. Additional properties cf such groups are included. 相似文献
9.
本文给出了Hardy-Littlewood极大函数和加权BMO的有界性证明:即若f∈BMOw,w∈A∞,且(?)Mf(x)<∞, 则M(f)(x) ∈BMOw, 且‖Mf‖w*≤c‖f‖w*. 相似文献
10.
Let X be a Banach space, (xn, Fn, n<- 1) a X-valued adapted sequence on probability space (Q, F, P) . Let T be all stopping times with respect to(Fn,n < - 1) . (xn, Fn,n< - 1) is called a T- uniform amart if there exists a t0∈T such that for each t∈T with t0,E‖xt‖<∞ and if (?)=0.In this paper we prove that. 相似文献