In mathematics, an operator is a function, usually of a special kind depending on the topic. For instance, in linear algebra an "operator" is a linear operator. In analysis an "operator" may be a differential operator, generalizing the ordinary derivative, or an integral operator, generalizing ordinary integration. Often, an "operator" is a function that acts on functions to produce other functions; or it may be a generalization of such a function, as in linear algebra, where some of the terminology reflects the origin of the subject in operations on the functions that are solutions of differential equations. One often thinks of an operator as dynamic, changing something into something else, whence the name; but this is only a way of thinking and not a formal definition.
An operator name or operator symbol is a notation that denotes a particular operator. When there is no danger of confusion, an operator name or operator symbol may be referred to more briefly as an "operator". Strictly speaking, however, the operator is a mathematical object and not the syntactic entity that denotes it. The reason for identifying it with its notation is that there are some operators that have come to have standard notations.
An example of an operator, specifically a differential operator, is the derivative itself. The corresponding operator name D, when placed before a differentiable function f, indicates that the function is to be differentiated with respect to the variable.
Gray Skies Ahead For Alcoa Ruthie Ackerman Tue, 07 Oct 2008 23:35:00 -0000 The aluminum producer announces grim Q3 results. Cleveland-Cliffs Nears Buyout Ruthie Ackerman Sat, 04 Oct 2008 07:00:00 -0000 The iron ore miner voted against its largest shareholder, Harbinger, raising its stake. Timken Tantalizes Investors Ruthie Ackerman Wed, 01 Oct 2008 04:03:00 -0000 The maker of bearings and alloys raised its third-quarter guidance, but is maintaining its fourth-quarter outlook.
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Stock markets retreat after rally Wed, 15 Oct 2008 07:33:17 -0000 After dramatic rises earlier in the week, most European and Asian stock markets give up some ground. Bank crisis to dominate EU talks Wed, 15 Oct 2008 08:55:52 -0000 EU leaders are to discuss multi-billion-euro rescue plans for Europe's ailing banks at a two-day summit in Brussels.
New York 'faces 165,000 job cuts' Wed, 15 Oct 2008 08:48:49 -0000 New York City could lose 165,000 jobs as a result of the crisis in the financial sector, the city's chief financial officer warns.
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Bleak Numbers Stoke Fears of Recession in Europe Wed, 15 Oct 2008 05:12:57 -0000 With the financial sector’s problems weighing directly on the broader economy, many economists say Europe is already in recession and will be lucky to get out of it by summer.
Europe and Asia Fail to Sustain Rallies Wed, 15 Oct 2008 08:52:07 -0000 Stocks fell in Europe after a mixed session in Asia as investors began to face the likelihood that dislocations would plague the economy even if bailouts were to succeed.
Despite Big Rally, Grim Outlook on Profits and Jobs Wed, 15 Oct 2008 07:32:15 -0000 A day after the stock market staged one of its biggest rallies in history, investors retreated once again.
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Unions, workers uneasy at possible GM, Chrysler deal Reuters Tue, 14 Oct 2008 21:22:55 -0400 DETROIT (Reuters) - Labor unions in the United States and Canada on Tuesday expressed concern about the prospect of job losses from any merger between General Motors Corp (GM.N) and Chrysler LLC, adding that union leaders had not been consulted by the automakers. Obama says he would act fast on $25 billion auto loans Reuters Tue, 14 Oct 2008 20:14:50 -0400 OREGON, Ohio/WASHINGTON (Reuters) - Democrat Barack Obama said on Tuesday that as president he would demand that up to $25 billion in government loans targeted for distressed U.S. automakers be distributed quickly. Boeing strike likely to run into November at least AP Tue, 14 Oct 2008 18:49:33 -0400 SEATTLE -- With the collapse of revived contract talks after barely two days, a strike that shut down Boeing Co.'s commercial aircraft plants Sept. 6 appears likely to continue well into November and possibly longer. Nikkei surges over 14 percent in record 1-day gain Reuters Tue, 14 Oct 2008 03:06:38 -0400 TOKYO (Reuters) - The Nikkei average soared more than 14 percent on Tuesday, the biggest one-day gain in its 58-year history, after governments around the world pledged to support struggling banks and restore confidence in the financial system. Boeing, striking machinists' talks break down AP Tue, 14 Oct 2008 00:41:20 -0400 SEATTLE -- Boeing Co. says renewed negotiations with its striking machinists broke down over an issue crucial to the company's "long-term competitiveness." A labor leader says the union was being asked to bargain away 2,000 jobs. Companies Hobbled by Uncertainty Steven Mufson Tue, 14 Oct 2008 00:00:00 -0400 There was no outbreak of relief yesterday for a wide variety of American corporations that are still facing tight credit markets, uncertain economic prospects and fluctuating stock prices.
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