共查询到20条相似文献,搜索用时 55 毫秒
1.
Consider two F q -subspaces A and B of a finite field, of the same size, and let A ?1 denote the set of inverses of the nonzero elements of A. The author proved that A ?1 can only be contained in A if either A is a subfield, or A is the set of trace zero elements in a quadratic extension of a field. Csajbók refined this to the following quantitative statement: if A ?1 ? B, then the bound |A ?1∩B| ≤ 2|B|/q ? 2 holds. He also gave examples showing that his bound is sharp for |B| ≤ q 3. Our main result is a proof of the stronger bound |A ?1 ∩ B| ≤ |B|/q · (1 + O d (q ?1/2)), for |B| = q d with d > 3. We also classify all examples with |B| ≤ q 3 which attain equality or near-equality in Csajbók’s bound. 相似文献
2.
P. Chansangiam 《Journal of Mathematical Analysis and Applications》2009,356(2):525-276
Let B(H) be the space of all bounded linear operators on a complex separable Hilbert space H. Bohr inequality for Hilbert space operators asserts that for A,B∈B(H) and p,q>1 real numbers such that 1/p+1/q=1,
2|A+B|?p2|A|+q2|B| 相似文献
3.
Under certain constraints on the characteristic of a field , the commutative standard enveloping q-algebra >B of a commutative triple system A over is defined. It is proved that(1) if the algebra B is simple, then the system A is simple;(2) if the system A is simple, then B either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals). 相似文献
4.
Rajendra Bhatia 《印度理论与应用数学杂志》2010,41(1):99-111
Lipschitz continuity of the matrix absolute value |A| = (A*A)1/2 is studied. Let A and B be invertible, and let M
1 = max(‖A‖, ‖B‖), M
2 = max(‖A
−1‖, ‖B
−1‖). Then it is shown that
$
\left\| { \left| A \right| - \left| B \right| } \right\| \leqslant \left( {1 + log M_1 M_2 } \right) \left\| {A - B} \right\|
$
\left\| { \left| A \right| - \left| B \right| } \right\| \leqslant \left( {1 + log M_1 M_2 } \right) \left\| {A - B} \right\|
相似文献
5.
It is proved that for any two subsets A and B of an arbitrary finite field $
\mathbb{F}_q
$
\mathbb{F}_q
such that |A||B| > q, the identity 10AB = $
\mathbb{F}_q
$
\mathbb{F}_q
holds. Under the assumption |A||B| ⩾2q, this improves to 8AB = $
\mathbb{F}_q
$
\mathbb{F}_q
. 相似文献
6.
Eliyahu Beller 《Israel Journal of Mathematics》1975,22(1):68-80
The functionf(z), analytic in the unit disc, is inA p if \(\int {\int {_{\left| z \right|< 1} \left| {f(z)} \right|^p dxdy< \infty } } \) . A necessary condition on the moduli of the zeros ofA p functions is shown to be best possible. The functionf(z) belongs toB p if \(\int {\int {_{\left| z \right|< 1} \log ^ + \left| {f(z)} \right|)^p } } \) . Let {z n } be the zero set of aB p function. A necessary condition on |z n | is obtained, which, in particular, implies that Σ(1?|z n |)1+(1/p)+g <∞ for all ε>0 (p≧1). A condition on the Taylor coefficients off is obtained, which is sufficient for inclusion off inB p. This in turn shows that the necessary condition on |z n | is essentially the best possible. Another consequence is that, forq≧1,p<q, there exists aB p zero set which is not aB q zero set. 相似文献
7.
Mitsuru Uchiyama 《Integral Equations and Operator Theory》2000,37(1):95-105
LetA, B be bounded selfadjoint operators on a Hilbert space. We will give a formula to get the maximum subspace
such that
is invariant forA andB, and
. We will use this to show strong monotonicity or strong convexity of operator functions. We will see that when 0≤A≤B, andB−A is of finite rank,A
t
≤B
t
for somet>1 if and only if the null space ofB−A is invariant forA. 相似文献
8.
Fuad Kittaneh 《Integral Equations and Operator Theory》2010,68(4):519-527
Let A, B, and X be operators on a complex separable Hilbert space such that A and B are positive, and let 0 ≤ v ≤ 1. The Heinz inequalities assert that for every unitarily invariant norm | | | ·| | | ,{\left\vert \left\vert \left\vert \cdot \right\vert \right\vert \right\vert ,}
|