The Peterson Institute for International Economics has this short piece on their web site, There Is No Liquidity Trap: Understanding 21st Century Monetary Policy.
As long as there exist assets whose price would be pushed up (and rate of return pushed down) by extra demand, monetary policy remains effective and there is no liquidity trap. Fiscal policy may be a useful alternative or complement to monetary policy in certain circumstances, but it is not a necessary alternative even when the short-term risk-free interest rate is zero.
There is no reason to doubt that central bank purchases of equity or real estate could significantly influence the prices of those assets.
I was thinking of all the arguments against these ideas, and wondering if I needed to broaden my thinking to accept what this author, Joseph E. Gagnon, was saying. Then I started to think beyond the examples of equity and real estate. The Fed could buy roads and bridges. At this point I realized why monetary policy could do all the things that we think only fiscal policy can do. You just change your definition of monetary policy to include all the things in fiscal policy, and then everything becomes possible.
The official explanation of the Peterson Institute says:
The Peterson Institute for International Economics is a private, nonprofit, nonpartisan research institution devoted to the study of international economic policy.
While The Peterson Institute does employ some very respectable economists, I am always a little suspicious of the Institute because of some of the strongly held, and wacky, economic ideas held by the founder and money bags behind the institute, Pete Peterson.
It might be very interesting and worthwhile to follow up the links to citations in the article.