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Suppose that is a Banach space over K. A subspace M of is said to be complemented in if there exists a subspace N of such that =M N, that is if , then there exists in M and in N such that , and M N . Prove that each finite dimensional subspace of is complemented in .
Hint: Suppose that M is a finite dimensional subspace of and is a basis for M. Define linear functionals : M K by for in K, k=1,2,...,n. Apply the Hahn-Banach Theorem, and look at the kernels of the linear functionals.
Find how many hours of labor did it take to repair the car.
An item costs $1300 , has a scrap value of $100, and a useful life of six years.
Find the cost to remove the pollutant
Set up the objective function & constraints & then solve.
Show that an equation of the tangent to C at P is y = 2x - 2 √2 + In(3+ 2√2). The tangent to C at the point Q is parallel to the tangent to Cat P.
A)Evaluate the expression.15P2B)In how many ways can a chairperson and a vice chairperson be selected from a committee of 25 senators?C)Evaluate the expression.
The steps are: (a) Move the constant term to the right side of the equation (b) Multiply each term in the equation by four times the coefficient of the x2 term (c) Square the coefficient of the original x term and add it to both sides of the equat..
Find the level of pollution at 9am, 11am, 5pm, 7pm, midnight, Graph y = P(t) and From the graph in part (f), at what time(s) is the pollution level highest? Lowest?
Use radical notation to rewrite the expression.1/2 (small 1/2 just above and to the right of 16)16 =16 1/2 (small 1/2 just above and to the right of 16) =
Determine the equation of the line, in slope- intercept form that is parallel to 5x+4y = -3 and contains (-8,9). Find the equation of the line through the point (-2,6) and perpendicular to y= (3/5)x -2
Please complete the following question: Use the quadratic formula to solve the equation. x^2 - x = -5. Make sure to show all necessary steps.
In regards to the Western context, is there a point at which the level of inequality becomes so great that it is detrimental for individuals trying to improve their situation and to the future of the society as a whole?a
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